Finite semiprimitive permutation groups of rank 3
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Cai Heng Li
Abstract
A transitive permutation group is called semiprimitive if each of its normal subgroups is either semiregular or transitive. The class of semiprimitive groups properly includes primitive groups, quasiprimitive groups and innately transitive groups. The latter three classes of rank 3 permutation groups have been classified, making significant progress towards solving the long-standing problem of classifying permutation groups of rank 3. In this paper, we complete the classification of finite semiprimitive groups of rank 3, building on the recent work of Huang, Li and Zhu. Examples include Schur coverings of certain almost simple 2-transitive groups and three exceptional small groups.
Acknowledgements
The authors are grateful to the anonymous referees for their valuable comments and suggestions that have helped to improve the paper.
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Communicated by: Michael Giudici
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