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Lie rings of groups of prime exponent

Part of: Lie algebras and Lie superalgebras Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

M. R. Vaughan-Lee
M. R. Vaughan-Lee
Affiliation:
Christ ChurchOxford OX1 1DPEngland
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Abstract

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We investigate the identities which hold in the associated Lie rings of groups of prime exponent. The multilinear identities which hold in these Lie rings are known, and it is conjectured that all the identities which hold in these Lie rings are consequences of multilinear ones. This is known to be the case for the associated Lie rings of two generator groups of exponent 5, and we provide some additional avidence for the conjecture by confirming that it also holds true for the associated Lie rings of three generator groups of exponent five.

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups 17B60: Lie (super)algebras associated with other structures (associative, Jordan, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 3 , December 1990 , pp. 386 - 398
Copyright
Copyright © Australian Mathematical Society 1990

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