Further Group-Theoretic Properties of Polycyclic Groups

  • B. A. F. WehrfritzEmail author
Part of the Algebra and Applications book series (AA, volume 10)


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.


Normal Subgroup Maximal Subgroup Nilpotent Group Abelian Subgroup Soluble Group 
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Copyright information

© Springer-Verlag London 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesQueen Mary, University of LondonLondonUK

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