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arXiv · 2106.04472

The growth of abelian sections

Luca Sabatini
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Abstract

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

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Luca Sabatini. 2021-06-08. The growth of abelian sections. https://doi.org/10.1007/s10231-022-01276-w

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