On the minimal degree of a transitive permutation group with stabilizer a 2-group

The minimal degree of a permutation group is defined as the minimal number of non-fixed points of a non-trivial element of . In this paper, we show that if is a transitive permutation group of degree having no non-trivial normal 2-subgroups such that the stabilizer of a point is a 2-group, then the...

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Bibliographic Details
Published inJournal of group theory Vol. 24; no. 3; pp. 619 - 634
Main Authors Potočnik, Primož, Spiga, Pablo
Format Journal Article
LanguageEnglish
Published Berlin Walter de Gruyter GmbH 01.05.2021
Subjects
Image classification
Permutations
Subgroups
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Summary:The minimal degree of a permutation group is defined as the minimal number of non-fixed points of a non-trivial element of . In this paper, we show that if is a transitive permutation group of degree having no non-trivial normal 2-subgroups such that the stabilizer of a point is a 2-group, then the minimal degree of is at least . The proof depends on the classification of finite simple groups.
ISSN:1433-5883
1435-4446
DOI:10.1515/jgth-2020-0058