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Another Proof of Gluck's Theorem

✍ Scribed by Hiroshi Matsuyama

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 56 KB
Volume: 247
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9026

No coin nor oath required. For personal study only.

✦ Synopsis

In this article, G is a permutation group on a finite set . We write permutations on the right, so that αg is the image of α ∈ by the action of g ∈ G. A subset S of is said to be G-regular if the stabilizer g ∈ G Sg = S is the identity.

Our purpose is to give a direct short proof of the following theorem by Gluck [3, Corollary 3.3].

Gluck's Theorem. Let G be a permutation group of odd order on a finite set . Then G has a regular subset in .

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