A quasigroup with an identity element is called a loop.
Definitions
There are at least two equivalent formal definitions of quasigroup. One defines a quasigroup as a set with one binary operation, and the other, from universal algebra, defines a quasigroup as having three primitive operations. We begin with the first definition.
A quasigroup(Q, ∗) is a set, Q, with a binary operation, ∗, (that is, a magma), obeying the Latin square property. This states that, for each a and b in Q, there exist unique elements x and y in Q such that both
a ∗ x = b
y ∗ a = b
hold. (In other words: Each element of the set occurs exactly once in each row and exactly once in each column of the quasigroup's multiplication table, or Cayley table. This property ensures that the Cayley table of a finite quasigroup is a Latin square.)
Groupoid || Quasi Group|| Binary operation || Groupoid with examples
Here we introduced the concept of Groupoid. We tried it to understand with set of natural number and set of integer.
published: 02 Nov 2023
Quasigroups, Loops and some of their Applications
Brandon University
Faculty of Science Seminar Series
2023-24
https://www.brandonu.ca/science/seminar-series/
January 26, 2024
Jaiyéolá Tèmitópé Gbóláhàn
Obafemi Awolowo University
Nigeria
Quasigroups, Loops and some of their Applications
Abstract:
This is an overview of the theory of quasigroups and loops. Notions and concepts which are commonly used in their studies will be discussed. An historical background of the theory of quasigroup and loop across the globe will be done. Some varieties and classes of quasigroups and loops, their algebraic properties, and applications to various aspects of science will be discussed.
Biography:
I obtained a BSc degree in Mathematical Sciences (with bias in Mathematics) in 2002, MSc degree in Mathematics in 2005 and PhD degree in Mathematics in 2009...
published: 06 Feb 2024
What does quasigroup mean?
What does quasigroup mean?
A spoken definition of quasigroup.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/quasigroup
Text to Speech powered by TTS-API.COM
published: 10 Apr 2015
How to Pronounce Quasigroup
This video shows you how to pronounce Quasigroup
published: 01 Jun 2015
Groupoid | Semi Group | Quasi group | Group Theory by DR Colleger
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grou...
published: 23 Jul 2023
Quasigroup
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Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible.Quasigroups differ from groups mainly in that they need not be associative.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
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published: 22 Jan 2016
Quasi group ||groupoid ||semi group ||Abstract algebra ||lecture no - 03||Bengali medium ||S M sir
What is Quasi group?? Definition of quasi group? Examples of quasi group. What is groupoid? What is semi group? What is monoid? Examples of semi group. Examples of groupoid. Example of monoid. Group theory in abstract algebra in mathematics. 3rd lecture in abstract algebra by sm sir...
published: 11 May 2020
What is Quasi group? Class 11 SOCIOLOGY Ch.2
published: 10 Jun 2022
Jack Allsop, “Solution to a question of Falconer on quasigroup varieties”
published: 19 Nov 2021
Group definitions | Quasi group | Semi group | Monoid | Group Theory Course
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Brandon University
Faculty of Science Seminar Series
2023-24
https://www.brandonu.ca/science/seminar-series/
January 26, 2024
Jaiyéolá Tèmitópé Gbóláhàn
Obafem...
Brandon University
Faculty of Science Seminar Series
2023-24
https://www.brandonu.ca/science/seminar-series/
January 26, 2024
Jaiyéolá Tèmitópé Gbóláhàn
Obafemi Awolowo University
Nigeria
Quasigroups, Loops and some of their Applications
Abstract:
This is an overview of the theory of quasigroups and loops. Notions and concepts which are commonly used in their studies will be discussed. An historical background of the theory of quasigroup and loop across the globe will be done. Some varieties and classes of quasigroups and loops, their algebraic properties, and applications to various aspects of science will be discussed.
Biography:
I obtained a BSc degree in Mathematical Sciences (with bias in Mathematics) in 2002, MSc degree in Mathematics in 2005 and PhD degree in Mathematics in 2009 at the University of Agriculture, Abeokuta,
Nigeria (now Federal University of Agriculture, Abeokuta, Nigeria). My MSc and PhD theses were based on the notions of "Central Loops" and "Osborn Loops" in the field of Algebra known as "Theory of Quasigroups and Loops". After my graduate studies at the Federal University of Agriculture, Abeokuta, I got an appointment at the Department of Mathematics, Faculty of Science, Obafemi Awolowo University (OAU), Ile-Ife, Nigeria in 2006 and have since risen to the position of a full Professor in 2017. I have been teaching Algebra courses at undergraduate and post graduate levels, supervised nine Masters of Science theses in Mathematics and supervised 7 PhD theses in Mathematics. I have attended national and International Conferences and Schools in the past and been involved in the organization of others. I am a Fellow of the Nigerian Young Academy (FNYA), Editor (Mathematical Sciences Section) of Annals of Science and Technology, Published by Nigerian Young Academy (NYA), Editor, International Journal of Mathematical Sciences and Optimization: Theory and Applications and International Ambassador of Africa Project Against Suicide (APAS). I am the Head of Nigerian Branch of Neutrosophic Science International Association (NSIA), University of New Mexico, United States of America and the Director for Human Resources, Platinum Minds Global Company (PMGC). I have published not less than eighty five (85) journal articles; authored a book; co-authored another book; reviewed seven (7) books; and
contributed to seven (7) books. I specialize in the areas of Algebra called "Groups and their Generalization" and "Non-Associative Algebraic Systems". My particular field of expertise is in the "Theory of Groupoids, Quasigroups and Loops". I also work on "Neutrosophic Algebraic Structures" and "Non-Associative Hyper-Algebraic Structures" and "Soft Quasigroup". I am enthusiastic to apply these areas of studies to Cryptography, Coding Theory, Sociology, Sports and Biological Inheritance. I am a member of the professional organizations Nigerian Mathematical Society (NMS), African Mathematical Union (AMU) and American Mathematical Society (AMS). I have served as referee for scholarly journals
both nationally and internationally since 2009. I am a reviewer for the Mathematical Reviews (MathSciNet) and Zentralblatt MATH (ZbMATH Open). I have won national and international awards. Among which are the International Mathematical Union (IMU) Awards (EUR 1147,08=$1470) for the International Congress of Mathematicians (ICM) in 2010 and International Mathematical Union (IMU), Chebyshev Grant, for the International Congress of Mathematicians (ICM) in 2022. As a member of the Nigerian Young Academy (NYA) executive, I won a 5,000 USD TWAS-ROSSA grant (2016), 25,000 USD IAP- CAREGIE small grant (2017-2018) and USD 4,000-6,000 IAP grant (2018).
Brandon University
Faculty of Science Seminar Series
2023-24
https://www.brandonu.ca/science/seminar-series/
January 26, 2024
Jaiyéolá Tèmitópé Gbóláhàn
Obafemi Awolowo University
Nigeria
Quasigroups, Loops and some of their Applications
Abstract:
This is an overview of the theory of quasigroups and loops. Notions and concepts which are commonly used in their studies will be discussed. An historical background of the theory of quasigroup and loop across the globe will be done. Some varieties and classes of quasigroups and loops, their algebraic properties, and applications to various aspects of science will be discussed.
Biography:
I obtained a BSc degree in Mathematical Sciences (with bias in Mathematics) in 2002, MSc degree in Mathematics in 2005 and PhD degree in Mathematics in 2009 at the University of Agriculture, Abeokuta,
Nigeria (now Federal University of Agriculture, Abeokuta, Nigeria). My MSc and PhD theses were based on the notions of "Central Loops" and "Osborn Loops" in the field of Algebra known as "Theory of Quasigroups and Loops". After my graduate studies at the Federal University of Agriculture, Abeokuta, I got an appointment at the Department of Mathematics, Faculty of Science, Obafemi Awolowo University (OAU), Ile-Ife, Nigeria in 2006 and have since risen to the position of a full Professor in 2017. I have been teaching Algebra courses at undergraduate and post graduate levels, supervised nine Masters of Science theses in Mathematics and supervised 7 PhD theses in Mathematics. I have attended national and International Conferences and Schools in the past and been involved in the organization of others. I am a Fellow of the Nigerian Young Academy (FNYA), Editor (Mathematical Sciences Section) of Annals of Science and Technology, Published by Nigerian Young Academy (NYA), Editor, International Journal of Mathematical Sciences and Optimization: Theory and Applications and International Ambassador of Africa Project Against Suicide (APAS). I am the Head of Nigerian Branch of Neutrosophic Science International Association (NSIA), University of New Mexico, United States of America and the Director for Human Resources, Platinum Minds Global Company (PMGC). I have published not less than eighty five (85) journal articles; authored a book; co-authored another book; reviewed seven (7) books; and
contributed to seven (7) books. I specialize in the areas of Algebra called "Groups and their Generalization" and "Non-Associative Algebraic Systems". My particular field of expertise is in the "Theory of Groupoids, Quasigroups and Loops". I also work on "Neutrosophic Algebraic Structures" and "Non-Associative Hyper-Algebraic Structures" and "Soft Quasigroup". I am enthusiastic to apply these areas of studies to Cryptography, Coding Theory, Sociology, Sports and Biological Inheritance. I am a member of the professional organizations Nigerian Mathematical Society (NMS), African Mathematical Union (AMU) and American Mathematical Society (AMS). I have served as referee for scholarly journals
both nationally and internationally since 2009. I am a reviewer for the Mathematical Reviews (MathSciNet) and Zentralblatt MATH (ZbMATH Open). I have won national and international awards. Among which are the International Mathematical Union (IMU) Awards (EUR 1147,08=$1470) for the International Congress of Mathematicians (ICM) in 2010 and International Mathematical Union (IMU), Chebyshev Grant, for the International Congress of Mathematicians (ICM) in 2022. As a member of the Nigerian Young Academy (NYA) executive, I won a 5,000 USD TWAS-ROSSA grant (2016), 25,000 USD IAP- CAREGIE small grant (2017-2018) and USD 4,000-6,000 IAP grant (2018).
What does quasigroup mean?
A spoken definition of quasigroup.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - K...
What does quasigroup mean?
A spoken definition of quasigroup.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/quasigroup
Text to Speech powered by TTS-API.COM
What does quasigroup mean?
A spoken definition of quasigroup.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/quasigroup
Text to Speech powered by TTS-API.COM
Groupoid | Semi Group | Quasi group | Group Theory | @drcolleger
My another channel for Competitive Mathematics:
https://www.youtube.com/c/SuperiorMathematics
...
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If you find our videos helpful you can support us by buying something from amazon.
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Quasigroup
In mathematics, espec...
If you find our videos helpful you can support us by buying something from amazon.
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Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible.Quasigroups differ from groups mainly in that they need not be associative.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
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https://www.youtube.com/watch?v=SSy6wobSKDE
If you find our videos helpful you can support us by buying something from amazon.
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Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible.Quasigroups differ from groups mainly in that they need not be associative.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=SSy6wobSKDE
What is Quasi group?? Definition of quasi group? Examples of quasi group. What is groupoid? What is semi group? What is monoid? Examples of semi group. Examples...
What is Quasi group?? Definition of quasi group? Examples of quasi group. What is groupoid? What is semi group? What is monoid? Examples of semi group. Examples of groupoid. Example of monoid. Group theory in abstract algebra in mathematics. 3rd lecture in abstract algebra by sm sir...
What is Quasi group?? Definition of quasi group? Examples of quasi group. What is groupoid? What is semi group? What is monoid? Examples of semi group. Examples of groupoid. Example of monoid. Group theory in abstract algebra in mathematics. 3rd lecture in abstract algebra by sm sir...
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Brandon University
Faculty of Science Seminar Series
2023-24
https://www.brandonu.ca/science/seminar-series/
January 26, 2024
Jaiyéolá Tèmitópé Gbóláhàn
Obafemi Awolowo University
Nigeria
Quasigroups, Loops and some of their Applications
Abstract:
This is an overview of the theory of quasigroups and loops. Notions and concepts which are commonly used in their studies will be discussed. An historical background of the theory of quasigroup and loop across the globe will be done. Some varieties and classes of quasigroups and loops, their algebraic properties, and applications to various aspects of science will be discussed.
Biography:
I obtained a BSc degree in Mathematical Sciences (with bias in Mathematics) in 2002, MSc degree in Mathematics in 2005 and PhD degree in Mathematics in 2009 at the University of Agriculture, Abeokuta,
Nigeria (now Federal University of Agriculture, Abeokuta, Nigeria). My MSc and PhD theses were based on the notions of "Central Loops" and "Osborn Loops" in the field of Algebra known as "Theory of Quasigroups and Loops". After my graduate studies at the Federal University of Agriculture, Abeokuta, I got an appointment at the Department of Mathematics, Faculty of Science, Obafemi Awolowo University (OAU), Ile-Ife, Nigeria in 2006 and have since risen to the position of a full Professor in 2017. I have been teaching Algebra courses at undergraduate and post graduate levels, supervised nine Masters of Science theses in Mathematics and supervised 7 PhD theses in Mathematics. I have attended national and International Conferences and Schools in the past and been involved in the organization of others. I am a Fellow of the Nigerian Young Academy (FNYA), Editor (Mathematical Sciences Section) of Annals of Science and Technology, Published by Nigerian Young Academy (NYA), Editor, International Journal of Mathematical Sciences and Optimization: Theory and Applications and International Ambassador of Africa Project Against Suicide (APAS). I am the Head of Nigerian Branch of Neutrosophic Science International Association (NSIA), University of New Mexico, United States of America and the Director for Human Resources, Platinum Minds Global Company (PMGC). I have published not less than eighty five (85) journal articles; authored a book; co-authored another book; reviewed seven (7) books; and
contributed to seven (7) books. I specialize in the areas of Algebra called "Groups and their Generalization" and "Non-Associative Algebraic Systems". My particular field of expertise is in the "Theory of Groupoids, Quasigroups and Loops". I also work on "Neutrosophic Algebraic Structures" and "Non-Associative Hyper-Algebraic Structures" and "Soft Quasigroup". I am enthusiastic to apply these areas of studies to Cryptography, Coding Theory, Sociology, Sports and Biological Inheritance. I am a member of the professional organizations Nigerian Mathematical Society (NMS), African Mathematical Union (AMU) and American Mathematical Society (AMS). I have served as referee for scholarly journals
both nationally and internationally since 2009. I am a reviewer for the Mathematical Reviews (MathSciNet) and Zentralblatt MATH (ZbMATH Open). I have won national and international awards. Among which are the International Mathematical Union (IMU) Awards (EUR 1147,08=$1470) for the International Congress of Mathematicians (ICM) in 2010 and International Mathematical Union (IMU), Chebyshev Grant, for the International Congress of Mathematicians (ICM) in 2022. As a member of the Nigerian Young Academy (NYA) executive, I won a 5,000 USD TWAS-ROSSA grant (2016), 25,000 USD IAP- CAREGIE small grant (2017-2018) and USD 4,000-6,000 IAP grant (2018).
What does quasigroup mean?
A spoken definition of quasigroup.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/quasigroup
Text to Speech powered by TTS-API.COM
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Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible.Quasigroups differ from groups mainly in that they need not be associative.
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What is Quasi group?? Definition of quasi group? Examples of quasi group. What is groupoid? What is semi group? What is monoid? Examples of semi group. Examples of groupoid. Example of monoid. Group theory in abstract algebra in mathematics. 3rd lecture in abstract algebra by sm sir...
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A quasigroup with an identity element is called a loop.
Definitions
There are at least two equivalent formal definitions of quasigroup. One defines a quasigroup as a set with one binary operation, and the other, from universal algebra, defines a quasigroup as having three primitive operations. We begin with the first definition.
A quasigroup(Q, ∗) is a set, Q, with a binary operation, ∗, (that is, a magma), obeying the Latin square property. This states that, for each a and b in Q, there exist unique elements x and y in Q such that both
a ∗ x = b
y ∗ a = b
hold. (In other words: Each element of the set occurs exactly once in each row and exactly once in each column of the quasigroup's multiplication table, or Cayley table. This property ensures that the Cayley table of a finite quasigroup is a Latin square.)