Solvable and Nilpotent Groups

Steven Roman

Chapter Chapter 11 in Fundamentals of Group Theory, 2012, pp 291-317 from Springer

Abstract: Abstract By a classKof groups, we mean a subclass of the class of all groups with the following two properties: 1)K contains a trivial group 2)K is closed under isomorphism, that is, $$G \ \epsilon \ \mathcal{K} and \ H \thickapprox \ G \Longrightarrow \ H \ \epsilon \ \mathcal{K}$$ For example, the abelian groups form a class of groups. A group of classK is called aK-group andK-group H that is a subgroup of a groupGis called a K- subgroup ofK. A classKis a trivial class if it contains only one-element groups.

Date: 2012
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DOI: 10.1007/978-0-8176-8301-6_11

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