group theory

English

Wikibooks

Alternative forms

• theory of groups

Noun

group theory (usually uncountable, plural group theories)

1. Used other than figuratively or idiomatically: see group,‎ theory; a theory about (particular kinds of) groups.
   • 2007, Hedley G. Dimock, Rachel R. Kass, How to Observe Your Group, Captus Press, 4th Edition, page 3,

     After you have read over the seven group theories you'll be clearer about what makes the most sense to you for the groups with which you want to use your observation skills.

   • 2012, Stéphanie Delaune, Steve Kremer, Daniel Pasaila, Security Protocols, Constraint Systems, and Group Theories, Bernhard Gramlich, Dale Miller, Ulrike Sattler (editors), Automated Reasoning: 6th International Joint Conference, Springer, LNAI 7364, page 165,

     In particular we study the case where cryptographic primitives are modelled using a group theory. Group theories are a special case of monoidal theories which have been extensively studied by F. Baader and W. Nutt [20,6] who have provided a complete survey of unification in these theories. Group theories include theories for exclusive or and Abelian groups.

2. (algebra, uncountable) The mathematical theory of groups.
   • 1968, Arthur P. Cracknell, editor, Applied Group Theory: Selected Readings in Physics, Pergamon Press, page ix:

     THE feeling seems to be developing among physicists that group theory can be used as and when required, as many other techniques already are, without its being necessary for everyone to study all the whys and wherefores of the mathematical details involved.

   • 1995, Jean Brocas, Chapter 4: The Use of Group Theory in the Study of Non-Rigid Molecules, Danail Bonchev, D. H. Rouvray (editors), Chemical Group Theory: Techniques and Applications, Gordon and Breach, page 133,

     Planar cis and/or trans internal rotation tunnelling have been discussed in terms of group theory, leading to theoretical spectra which have been compared to experimental work.

Related terms

• group theoretical

Translations

mathematical theory of groups

• Chinese:

  Mandarin: 群論／群论 (zh) (qúnlùn)

• Finnish: ryhmäteoria (fi)
• French: théorie des groupes f
• German: Gruppentheorie (de) f
• Hindi: समूह सिद्धांत (samūh siddhānt)
• Hungarian: csoportelmélet (hu)
• Icelandic: grúpufræði f
• Italian: teoria dei grupp f
• Japanese: 群論 (ja) (ぐんろん, gunron)
• Kazakh: топтар теориясы (toptar teoriäsy)
• Korean: 군론(群論) (gullon)
• Latin: theoria catervarum f
• Malay: teori kumpulan
• Portuguese: teoria dos grupos f
• Serbo-Croatian: teorija grupa f
• Spanish: teoría de grupos f
• Swedish: gruppteori c
• Tamil: குலக் கோட்பாடு (kulak kōṭpāṭu)
• Thai: ทฤษฎีกรุป
• Vietnamese: lý thuyết nhóm (理說𩁱)

See also

• Appendix:Glossary of group theory

Further reading

• List of group theory topics on Wikipedia.Wikipedia