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A NOTE ON PERMUTATION GROUPS AND THEIR REGULAR SUBGROUPS

Part of: Permutation groups Graph theory

Published online by Cambridge University Press:  01 October 2008

MING-YAO XU
MING-YAO XU*
Affiliation:
Department of Mathematics, Shanxi Normal University, Linfen, Shanxi 041004, People’s Republic of China (email: [email protected]) LMAM, Institute of Mathematics, Peking University, Beijing 100871, People’s Republic of China (email: [email protected])
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Abstract

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In this note we first prove that, for a positive integer n>1 with n≠p or p2 where p is a prime, there exists a transitive group of degree n without regular subgroups. Then we look at 2-closed transitive groups without regular subgroups, and pose two questions and a problem for further study.

Keywords

transitive permutation groupregular subgroupnon-Cayley number

MSC classification

Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 2 , October 2008 , pp. 283 - 287
Copyright
Copyright © 2008 Australian Mathematical Society

References

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