Lower Bounds for Representation Growth

TL;DR

This paper investigates the minimal growth rates of representations in finitely generated groups, especially profinite and pro-p groups, and explores the maximum multiplicities of character degrees in finite simple groups.

Contribution

It provides new lower bounds for representation growth and analyzes character degree multiplicities in finite simple groups.

Findings

Established lower bounds for representation growth in specific group classes.

Analyzed maximal multiplicities of character degrees in finite simple groups.

Connected representation growth with properties of finite simple groups.

Abstract

This article examines lower bounds for the representation growth of finitely generated (particularly profinite and pro-p) groups. It also considers the related question of understanding the maximal multiplicities of character degrees in finite groups, and in particular simple groups.