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Isomorphisms of Finite Cayley Digraphs of Bounded Valency

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

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 377 KB
Volume: 73
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1998.1820

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✦ Synopsis

Let G be a finite group, S a subset of G" [1], and let Cay(G, S ) denote the Cayley digraph of G with respect to S. If, for all subsets S, T of G"[1] of size at most m, Cay(G, S )$Cay(G, T) implies that S _ =T for some _ # Aut(G), then G is called an m-DCI-group. In this paper, we prove that, for m 2, all m-DCI-groups are of the form U_V, where ( |U |, |V |)=1, U is abelian and V belongs to an explicitly determined list of groups. Moreover Sylow subgroups of such groups satisfy some very restrictive conditions.

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