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Representing the Quotient Groups of a Finite Permutation Group

✍ Scribed by Derek F. Holt; Jacqueline Walton

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 207 KB
Volume: 248
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8961

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a permutation group of finite degree d. We prove that the product of the orders of the composition factors of G that are not alternating groups acting naturally, in a sense that will be made precise, is bounded by c d-1 /d, where c = 4 5. We use this to prove that any quotient G/N of G has a faithful permutation representation of degree at most c d-1 .  2002 Elsevier Science (USA)

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