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Alternating Groups Acting on Finite Linear Spaces

Published online by Cambridge University Press:  25 June 2003

Alan R. Camina ,
Peter M. Neumann  and
Cheryl E. Praeger
Alan R. Camina
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ. E-mail: [email protected]
Peter M. Neumann
Affiliation:
The Queen's College, Oxford OX1 4AW. E-mail: [email protected]
Cheryl E. Praeger
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. E-mail: [email protected]
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Abstract

This is a contribution to the study of line-transitive groups of automorphisms of finite linear spaces. Groups which are almost simple are of particular importance. In this paper almost simple line-transitive groups whose socle is an alternating group are classified. It is proved that the only alternating groups to occur are those of degrees 7 and 8, and that only one linear space occurs, namely a well-known space with 15 points and 35 lines. Although much of the proof exploits special properties of alternating groups, some general theory of groups acting line-transitively on finite linear spaces is developed.

Keywords

linear spaceprojective planeline-transitivealternating groupalmost simple grouppermutation group20B2505B05
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 87 , Issue 1 , July 2003 , pp. 29 - 53
Copyright
2003 London Mathematical Society

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