Local Theorems and Generalized Soluble Groups

Abstract

We recall from the definition in Section 6.1 that a class of generalized soluble groups is a class of groups X satisfying

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i.e. a finite X-group is soluble and every soluble group is an X-group. Numerous classes of generalized soluble groups have arisen in previous chapters. Here several more will be introduced and we will also attempt to summarize what is known and what is still unknown about their relationships.