EMBEDDING PERMUTATION GROUPS INTO WREATH PRODUCTS IN PRODUCT ACTION
نویسندگان
چکیده
منابع مشابه
Three Types of Inclusions of Innately Transitive Permutation Groups into Wreath Products in Product Action
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 correspond to the product action of a w...
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A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X o Y of two permutation classes X and Y is also closed, and we investigate classes Y with the property that, for any finitely based class X, the wreath product X o Y is also finitely based.
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This paper is concerned with finite primitive permutation groups G which are subgroups of wreath products W in product action and are such that the socles of G and W are the same. The aim is to explore how the study of such groups may be reduced to the study of smaller groups. The O'Nan-Scott Theorem (see Liebeck, Praeger, Saxl [12] for the most recent and detailed treatment) sorts finite primi...
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We study (G, 2)-arc-transitive graphs for innately transitive permutation groups G such that G can be embedded into a wreath product SymΓwr Sl acting in product action on Γ. We find two such connected graphs: the first is Sylvester’s double six graph with 36 vertices, while the second is a graph with 120 vertices whose automorphism group is Aut Sp(4, 4). We prove that under certain conditions n...
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There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding 'imprimitive wreath decomposition concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The r...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2012
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788712000110