Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T05:56:15.248Z Has data issue: false hasContentIssue false

Alternating Groups Acting on Finite Linear Spaces

Published online by Cambridge University Press:  25 June 2003

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]
Get access

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.

Type
Research Article
Copyright
2003 London Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)