Enumeration of Groups in Varieties of $A$-groups: A survey

Geetha Venkataraman

Enumeration of Groups in Varieties of $A$-groups: A survey

Group Theory 2019-11-06 v1

Authors: Geetha Venkataraman

Abstract

Let $S$ be a class of groups and let $f_S (n)$ be the number of isomorphism classes of groups in $S$ of order $n$ . Let $f(n)$ count the number of groups of order $n$ up to isomorphism. The asymptotic bounds for $f(n)$ behave differently when restricted to abelian groups, $A$ -groups and groups in general. We survey some results and some open questions in enumeration of finite groups with a focus on enumerating within varieties of $A$ -groups.

Keywords

enumeration of groups a-groups varieties of groups isomorphism classes asymptotic bounds finite groups

Cite

@article{arxiv.1911.01924,
  title  = {Enumeration of Groups in Varieties of $A$-groups: A survey},
  author = {Geetha Venkataraman},
  journal= {arXiv preprint arXiv:1911.01924},
  year   = {2019}
}

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