Normal Structure of Groups

Ernest Shult () and David Surowski
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Ernest Shult: Kansas State University, Department of Mathematics

Chapter Chapter 5 in Algebra, 2015, pp 137-161 from Springer

Abstract: Abstract The Jordan-Hölder Theorem for Artinian Groups is a simple application of the poset-theoretic Jordan-Hölder Theorem expounded in Chap. 2 . A discussion of commutator identities is exploited in defining the derived series and solvability as well as in defining the upper and lower central series and nilpotence. The Schur-Zassenhaus Theorem for finite groups ends the chapter. In the exercises, one will encounter the concept of normally-closed families of subgroups of a group G, which gives rise to several well-known characteristic subgroups, such as $${\mathbf O}_p(G)$$ O p ( G ) , the torsion subgroup, and (when G is finite) the Fitting subgroup. Some further challenges appear in the exercises.

Keywords: Lower Central Series; Schur-Zassenhaus Theorem; Artin Groups; Commutator Identities; Characteristic Subgroup (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-19734-0_5

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