TY - JOUR

T1 - Isomorphisms of finite Cayley digraphs of bounded valency

AU - Li, Cai-Heng

AU - Praeger, Cheryl

AU - Xu, M.Y.

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

U2 - 10.1006/jctb.1998.1820

DO - 10.1006/jctb.1998.1820

M3 - Article

SN - 0095-8956

VL - 73

SP - 164

EP - 183

JO - Journal of combinatorial Theory Series B

JF - Journal of combinatorial Theory Series B

ER -