The growth of abelian sections

Abstract

Given an abstract group $G$, we study the function $a{b}_n(G):={\sup }_{|G:H|\le n}|H/[H,H]|$. If $G$ has no abelian composition factors, then $a{b}_n(G)$ is bounded by a polynomial: as a consequence, we find a sharp upper bound for the representation growth of these groups.

13 pages, final version

References in corpus (3)

• Nilpotent subgroups of class $2$ in finite groups
• Random Schreier graphs and expanders
• Abelian sections of the symmetric groups with respect to their index

Cited by in corpus (1)

• On groups with large verbal quotients