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On finite groups with the cayley isomorphism property

✍ Scribed by Li, Cai Heng; Praeger, Cheryl E.; Xu, Ming Yao

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 197 KB
Volume: 27
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199801)27:1<21::aid-jgt5>3.0.co;2-i

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T ⊂ G, Cay(G, S) ∼ = Cay(G, T ) implies S α = T for some α ∈ Aut(G), then Cay(G, S) is called a CI-graph of G. For a group G, if all Cayley digraphs of valency m are CI-graphs, then G is said to have the m-DCI property; if all Cayley graphs of valency m are CI-graphs, then G is said to have the m-CI property. It is shown that every finite group of order greater than 2 has a nontrivial CI-graph, and all finite groups with the m-CI property and with the m-DCI property are characterized for small values of m. A general investigation is made of the structure of Sylow subgroups of finite groups with the m-DCI property and with the m-CI property for large values of m.

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