Isomorphisms of finite Cayley digraphs of bounded valency

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    Abstract

    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 ail subsets S, T of G\(1) of size at most In. Cay(G, S) congruent to Cay(G, T) implies that S-sigma = T for some sigma is an element of Aut(G)1 then G is called an m-DCI-group. in this paper, we prove that, for m greater than or equal to 2, all m-DCI-groups are of the form U x V, where (\U\, \V\)= 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. (C) 1998 Academic Press.
    Original languageEnglish
    Pages (from-to)164-183
    JournalJournal of combinatorial Theory Series B
    Volume73
    DOIs
    Publication statusPublished - 1998

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