OFFSET
1,4
COMMENTS
See Slatterly references for precise definition of similarity classes and a proof of the first 12 terms.
See Betz and Nash for correction of a(10) and proof of terms 13-19.
LINKS
Alexander Betz and David A. Nash, Classifying groups with a small number of subgroups, arXiv:2006.11315 [math.GR], 2020.
Angsuman Das and Arnab Mandal, Solvability of a group based on its number of subgroups, arXiv:2403.01262 [math.GR], 2024.
George A. Miller, Groups having a small number of subgroups, Proc. Natl. Acad. Sci. U S A, vol. 25 (1939) 367-371.
David A. Nash and Alexander Betz, Classifying groups with a small number of subgroups, arXiv:2006.11315 [math.GR], 2020.
Michael C. Slattery, On a property motivated by groups with a specified number of subgroups, Amer. Math. Monthly, 123 (2016), 78-81.
Michael C. Slattery, Groups with at most twelve subgroups, arXiv:1607.01834 [math.GR], 2016.
EXAMPLE
For n = 6 the a(6) = 5 similarity classes of groups with 6 subgroups are Z_{p^5}, Z_p X Z_{q^2}, Z_3 X Z_3, S_3, Q_8.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Michael C Slattery, Jul 08 2016
EXTENSIONS
Correction of a(10) and extension to 19 terms by David A. Nash, Jun 29 2020
STATUS
approved