Neumann, Peter, Praeger, Cheryl and Smith, Simon
(2017)
Some infinite permutation groups and related finite linear groups.
Journal of the Australian Mathematical Society, 102
(1).
pp. 136149.
ISSN 14467887
Full content URL: http://doi.org/10.1017/S1446788716000343
Some infinite permutation groups and related finite linear groups   [Download] 

Preview 

PDF
2016 Some infinite permutation groups and related finite linear groupsFinalApprovedVersion.pdf
 Whole Document
304kB 
Item Type:  Article 

Item Status:  Live Archive 

Abstract
This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point stabilisers are merely assumed to satisfy minn, the minimal condition on normal subgroups. The groups G are then of two kinds. Either they have a maximal finite normal subgroup, modulo which they have either one or two minimal nontrivial normal subgroups, or they have a regular normal subgroup M which is a divisible abelian pgroup of finite rank. In the latter case the point stabilisers are finite and act irreducibly on a padic vector space associated with M. This leads to our second variation, which is a study of the finite linear groups that can arise.
Repository Staff Only: item control page