On classifying objects with specified groups of automorphisms, friendly subgroups, and Sylow tower groups
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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. We also classify the maximal partial spreads invariant under a group of order 5 in both PG(3, 7) and PG(3, 8).
- College Publications