Maximal representation dimension of finite p-groups

TL;DR

This paper determines the maximum possible representation dimension among all finite p-groups of a fixed order p^n, providing insights into the embedding complexity of such groups.

Contribution

It establishes the maximal representation dimension for all groups of order p^n, a new result in the study of p-group representations.

Findings

Maximum representation dimension for p-groups of order p^n identified

Provides bounds for embedding complexity of finite p-groups

Advances understanding of group embedding properties

Abstract

The representation dimension of a finite group G is the smallest positive integer m for which there exists an embedding of G in GL_m(C). In this paper we find the largest value of representation dimensions, as Granges over all groups of order p^n, for a fixed prime p and a fixed exponent n greater than zero.