Abstract
We have found numerous properties of finite groups which are equivalent to nilpotence—see especially 5.2.4. For example, normality of all the Sylow subgroups in such a property. When applied to infinite groups, these properties are usually much weaker, giving rise to a series of wide generalizations of nilpotence. For soluble groups the situation is similar. The aim of this chapter is to discuss the main types of generalized nilpotent and soluble groups and their interrelations.
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© 1993 Springer-Verlag New York, Inc.
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Robinson, D.J.S. (1993). Generalizations of Nilpotent and Soluble Groups. In: A Course in the Theory of Groups. Graduate Texts in Mathematics, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0128-8_12
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DOI: https://doi.org/10.1007/978-1-4684-0128-8_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94092-2
Online ISBN: 978-1-4684-0128-8
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