The classification of 3/2-transitive permutation groups and 1/2-transitive linear groups
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Accepted version
Author(s)
Liebeck, MW
Praeger, CE
Saxl, J
Type
Journal Article
Abstract
A linear group G ≤ GL(V ), where V is a finite vector space, is called 12
-transitive if all the G-orbits on the set of nonzero vectors have the same size. We complete the classification of all the 12-transitive linear groups. As a consequence we complete the determination of the finite 32-transitive permutation groups – the transitive groups for which a point-stabilizer
has all its nontrivial orbits of the same size. We also determine the (k +1
2)-transitive groups for integers k ≥ 2.
-transitive if all the G-orbits on the set of nonzero vectors have the same size. We complete the classification of all the 12-transitive linear groups. As a consequence we complete the determination of the finite 32-transitive permutation groups – the transitive groups for which a point-stabilizer
has all its nontrivial orbits of the same size. We also determine the (k +1
2)-transitive groups for integers k ≥ 2.
Date Issued
2019-09-23
Date Acceptance
2016-04-15
Citation
Proceedings of the American Mathematical Society, 2019, 147, pp.5023-5037
ISSN
1088-6826
Publisher
American Mathematical Society
Start Page
5023
End Page
5037
Journal / Book Title
Proceedings of the American Mathematical Society
Volume
147
Copyright Statement
© Copyright 2019 American Mathematical Society
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
0101 Pure Mathematics
Publication Status
Published
Date Publish Online
2019-09-23