The minimal degree of permutation representations of finite groups
Group Theory
2012-04-10 v1
Abstract
In this thesis we study the following property of a finite group G: the minimal number n such that G embeds in Sn. We start with an explicit formula for the number n for abelian groups. Then, we study the behavior of this group property in respect to direct products. Finally, we define and explore the "compression ratio" of a finite group G which measures how much better the best embedding is relative to the embedding given by Cayley's theorem.
Keywords
Cite
@article{arxiv.1204.1668,
title = {The minimal degree of permutation representations of finite groups},
author = {Oren Becker},
journal= {arXiv preprint arXiv:1204.1668},
year = {2012}
}