JournalspmVol. 74, No. 3pp. 233–242

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

  • Leonard H. Soicher

    Queen Mary University of London, UK
On classifying objects with specified groups of automorphisms, friendly subgroups, and Sylow tower groups cover

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Abstract

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 HH of a group KK is a friendly subgroup of KK if every subgroup of KK isomorphic to HH is conjugate in KK to HH. We explore easy-to-test sufficient conditions for a subgroup HH to be a friendly subgroup of a finite group KK, and for this, present an algorithm for determining whether a finite group HH is a Sylow tower group. We also classify the maximal partial spreads invariant under a group of order 55 in both PG(3,7) and PG (3,8).

Cite this article

Leonard H. Soicher, On classifying objects with specified groups of automorphisms, friendly subgroups, and Sylow tower groups. Port. Math. 74 (2017), no. 3, pp. 233–242

DOI 10.4171/PM/2004