
Published online:
31 October 2023
Published in print:
07 October 1993
Online ISBN:
9781383026221
Print ISBN:
9780198537861
Contents
Chapter
2 The associated Lie ring of a group
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Pages
26–52
-
Published:October 1993
Cite
Vaughan-Lee, Michael, 'The associated Lie ring of a group', The Restricted Burnside Problem (Oxford , 1993; online edn, Oxford Academic, 31 Oct. 2023), https://doi.org/10.1093/oso/9780198537861.003.0002, accessed 7 May 2025.
Abstract
In this chapter we introduce the associated Lie ring of a group. Most of the detailed information we obtain in later chapters about finite groups of prime-power exponent will come from studying their associated Lie rings, and studying the identities which these Lie rings satisfy. First, we establish some of the basic facts we need about the lower central series and the lower exponent-p-central series of a group. We then define the associated Lie ring of a group, describe some of its properties, and go on to determine an explicit basis for the multilinear identities which hold in the associated Lie rings of groups of prime-power exponent.
Subject
Pure Mathematics
Collection:
Oxford Scholarship Online
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