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Character degree graphs of automorphism groups of characteristically simple groups

✍ Scribed by Lewis, Mark L.; McVey, John K.

Book ID: 124054385
Publisher: Walter de Gruyter GmbH & Co. KG
Year: 2009
Tongue: English
Weight: 100 KB
Volume: 12
Category: Article
ISSN: 1433-5883
DOI: 10.1515/JGT.2008.083

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📜 SIMILAR VOLUMES

Character degree graphs of automorphism

Character degree graphs of automorphism groups of characteristically simple groups

✍ Lewis, Mark L.; McVey, John K. 📂 Article 📅 2009 🏛 Walter de Gruyter GmbH & Co. KG 🌐 English ⚖ 100 KB

Throughout this note, G will be a finite group, IrrðGÞ will be the set of irreducible characters of G, cdðGÞ will be the set of character degrees of G, and rðGÞ will be the set of primes that divide degrees in cdðGÞ. The prime vertex degree graph of G, written DðGÞ, is the graph with rðGÞ as its ver

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We solve some factorisation problems for finite characteristically simple groups, using factorisations of elementary abelian 2-groups. The problems arose from a study of permutation groups. We found the connection between the factorisations of these two types of groups surprisingly interesting.

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For a large class of finite Cayley graphs we construct covering graphs whose automorphism groups coincide with the groups of lifted automorphisms. As an application we present new examples of 1Â2-transitive and 1-regular graphs.