TY - JOUR

T1 - On finite groups with the Cayley isomorphism property

AU - Li, Cai-Heng

AU - Praeger, Cheryl

AU - Xu, M.Y.

PY - 1998

Y1 - 1998

N2 - Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T subset of G, Cay(G, S) congruent to Cay(G, T) implies S-alpha = T for some alpha is an element of 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 even/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. (C) 1998 John WiIey & Sons, Inc.

AB - Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T subset of G, Cay(G, S) congruent to Cay(G, T) implies S-alpha = T for some alpha is an element of 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 even/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. (C) 1998 John WiIey & Sons, Inc.

U2 - 10.1002/(SICI)1097-0118(199801)27:1<21::AID-JGT5>3.0.CO;2-I

DO - 10.1002/(SICI)1097-0118(199801)27:1<21::AID-JGT5>3.0.CO;2-I

M3 - Article

VL - 27

SP - 21

EP - 31

JO - Journal of Graph Theory

JF - Journal of Graph Theory

ER -