Abstract
Nilpotent groups lie between Abelian and soluble groups, and this second shorter chapter continues the work on these groups begun earlier. There is a surprising number of equivalent definitions which shows the importance of the notion. The second section discusses two ‘special’ subgroups of a group—the Frattini and Fitting subgroups; they have some remarkable properties (including being nilpotent), and extensions of the latter have proved useful in the completion of CFSG.
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© 2009 Springer-Verlag London
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Rose, H.E. (2009). Nilpotency. In: A Course on Finite Groups. Universitext. Springer, London. https://doi.org/10.1007/978-1-84882-889-6_10
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DOI: https://doi.org/10.1007/978-1-84882-889-6_10
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Publisher Name: Springer, London
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Online ISBN: 978-1-84882-889-6
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