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ON THE AUTOMORPHISM GROUPS OF CAYLEY GRAPHS OF FINITE SIMPLE GROUPS

Published online by Cambridge University Press:  24 March 2003

XIN GUI FANG
Affiliation:
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, Chinaxgfang@sxx0.math.pku.edu.cn, wangj@pku.edu.cn
CHERYL E. PRAEGER
Affiliation:
Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australiapraeger@maths.uwa.edu.au
JIE WANG
Affiliation:
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, Chinaxgfang@sxx0.math.pku.edu.cn, wangj@pku.edu.cn
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Abstract

Let $G$ be a finite nonabelian simple group and let $\Gamma$ be a connected undirected Cayley graph for $G$ . The possible structures for the full automorphism group ${\rm Aut}\Gamma$ are specified. Then, for certain finite simple groups $G$ , a sufficient condition is given under which $G$ is a normal subgroup of ${\rm Aut}\Gamma$ . Finally, as an application of these results, several new half-transitive graphs are constructed. Some of these involve the sporadic simple groups $G = J_1, J_4$ , Ly and BM, while others fall into two infinite families and involve the Ree simple groups and alternating groups. The two infinite families contain examples of half-transitive graphs of arbitrarily large valency.

Type
Notes and Papers
Copyright
© The London Mathematical Society, 2002

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