Abstract
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.
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© 2009 Springer-Verlag London
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Wehrfritz, B.A.F. (2009). Further Group-Theoretic Properties of Polycyclic Groups. In: Group and Ring Theoretic Properties of Polycyclic Groups. Algebra and Applications, vol 10. Springer, London. https://doi.org/10.1007/978-1-84882-941-1_5
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DOI: https://doi.org/10.1007/978-1-84882-941-1_5
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