Classifying groups with a small number of subgroups
Group Theory
2020-07-09 v3
Abstract
We provide lower bounds on the number of subgroups of a group as a function of the primes and exponents appearing in the prime factorization of . Using these bounds, we classify all abelian groups with 22 or fewer subgroups, and all non-abelian groups with 19 or fewer subgroups. This allows us to extend the integer sequence A274847 \cite{OEIS} introduced by Slattery in \cite{Slattery}.
Cite
@article{arxiv.2006.11315,
title = {Classifying groups with a small number of subgroups},
author = {David A. Nash and Alexander Betz},
journal= {arXiv preprint arXiv:2006.11315},
year = {2020}
}
Comments
12 pages, 3 tables; V2 Fixes an error (which has no effect on the final results) and also adds a few citations/details suggested by early readers; V3 fixes minor typographical errors and clarifies the explanation of Slattery's previous work