Some measures of finite groups related to permutation bases

TL;DR

This paper introduces three new measures to quantify the complexity of finite groups based on permutation bases and explores how these relate to existing measures.

Contribution

It defines novel measures of finite group complexity using permutation bases and analyzes their relationships with other known measures.

Findings

Proposes three measures of group complexity

Establishes relationships between new measures and existing ones

Provides insights into the structure of finite groups

Abstract

I define three "measures" of the complicatedness of a finite group in terms of bases in permutation representations of the group, and consider their relationships to other measures.