The minimal degree of permutation representations of finite groups

Oren Becker

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arXiv · 1204.1668

The minimal degree of permutation representations of finite groups

Oren Becker

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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.

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Oren Becker. 2012-04-07. The minimal degree of permutation representations of finite groups. https://arxiv.org/abs/1204.1668

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