On classifying objects with specified groups of automorphisms, friendly subgroups, and Sylow tower groups,Portugaliae Mathematica

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On classifying objects with specified groups of automorphisms, friendly subgroups, and Sylow tower groups
Portugaliae Mathematica ( IF 0.5 ) Pub Date : 2018-02-08 , DOI: 10.4171/pm/2004
Leonard Soicher ₁

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We describe some group theory which is useful in the classification of combinatorial objects having given groups of automorphisms. In particular, we show the usefulness of the concept of a friendly subgroup: a subgroup H of a group K is a friendly subgroup of K if every subgroup of K isomorphic to H is conjugate in K to H. We explore easy-to-test sufficient conditions for a subgroup H to be a friendly subgroup of a finite group K, and for this, present an algorithm for determining whether a finite group H is a Sylow tower group.

更新日期：2018-02-08

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