NDLI: Three types of inclusions of innately transitive permutation groups into wreath products in product action

Content Provider	Springer Nature Link
Author	Praeger, Cheryl E. Schneider, Csaba
Copyright Year	2007
Abstract	A permutation group is innately transitive if it has a transitive minimal normal subgroup, and this subgroup is called a plinth. In this paper we study three special types of inclusions of innately transitive permutation groups in wreath products in product action. This is achieved by studying the natural Cartesian decomposition of the underlying set that corresponds to the product action of the wreath product. Previously we identified six classes of Cartesian decompositions that can be acted upon transitively by an innately transitive group with a non-abelian plinth. The inclusions studied in this paper correspond to three of the six classes. We find that in each case the isomorphism type of the acting group is restricted, and some interesting combinatorial structures are left invariant. We also give a fairly general construction of inclusions for each type.
Starting Page	65
Ending Page	104
Page Count	40
File Format	PDF
ISSN	00212172
Journal	Israel Journal of Mathematics
Volume Number	158
Issue Number	1
e-ISSN	15658511
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics Algebra Group Theory and Generalizations Analysis Applications of Mathematics Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Three types of inclusions of innately transitive permutation groups into wreath products in product action