Abstract

In Chapter 5 we found numerous properties of finite groups which are equivalent nilpotence—see especially 5.2.4. For example, normality of all the Sylow subgroups is such a property. When applied to infinite groups, these properties are usually much weaker, giving rise to a series of wide generalizations of nilpotence. For soluble groups the situation is similar. The aim of this chapter is to discuss the main types of generalized nilpotent and soluble groups and their interrelations.KeywordsNormal SubgroupMaximal SubgroupNilpotent GroupMinimal Normal SubgroupSoluble GroupThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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