Further Group-Theoretic Properties of Polycyclic Groups
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In this chapter we continue our exposition from Chap. 2, but now we can make use of techniques developed in Chaps. 3 and 4.
We have already introduced the Frattini subgroup Φ(G) of a group G as the intersection of all the maximal subgroups of G, meaning G itself if none such exist. Also we proved in 1.17 that if G is finite then Φ(G) is nilpotent. Ito and Hirsch extended this as follows.
KeywordsNormal Subgroup Maximal Subgroup Nilpotent Group Abelian Subgroup Soluble Group
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