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PRIMITIVE PERMUTATION GROUPS WITH A COMMON SUBORBIT, AND EDGE-TRANSITIVE GRAPHS

Published online by Cambridge University Press:  06 March 2002

MARTIN W. LIEBECK ,
CHERYL E. PRAEGER  and
JAN SAXL
MARTIN W. LIEBECK
Affiliation:
Department of Mathematics, Imperial College, Huxley Building, 180 Queen's Gate, London SW7 2BZ [email protected]
CHERYL E. PRAEGER
Affiliation:
Department of Mathematics and Statistics, University of Western Australia, Perth, WA 6907, [email protected]
JAN SAXL
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB [email protected]
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Abstract

Dedicated to the memory of Helmut Wielandt

In this paper a classification is obtained of all pairs G, H of finite primitive permutation groups such that G < H, the socles of G and H are different, and G and H share a common non-trivial orbital. An application is given to the study of automorphism groups of edge-transitive graphs.

2000 Mathematical Subject Classification: 20B15, 20B25.

Keywords

primitive permutation groupssuborbitsorbitalsedge-transitive graphs
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 84 , Issue 2 , March 2002 , pp. 405 - 438
Copyright
2002 London Mathematical Society

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