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The Transfer of a Commutator Law from a Nil-Ring to its Adjoint Group

Published online by Cambridge University Press:  20 November 2018

David M. Riley  and
Vladimir Tasić
David M. Riley
Affiliation:
Department of Mathematics The University of Alabama Tuscaloosa, Alabama USA 35487-0350
Vladimir Tasić
Affiliation:
Department of Mathematics and Statistics University of New Brunswick Fredericton, New Brunswick E3B 5A3
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Abstract

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For every field F of characteristic p ≥ 0, we construct an example of a finite dimensional nilpotent F-algebra R whose adjoint group A(R) is not centreby- metabelian, in spite of the fact that R is Lie centre-by-metabelian and satisfies the identities x2p = 0 when p > 2 and x8 > 0 when p = 2. The existence of such algebras answers a question raised by A. E. Zalesskii, and is in contrast to positive results obtained by Krasilnikov, Sharma and Srivastava for Lie metabelian rings and by Smirnov for the class Lie centre-by-metabelian nil-algebras of exponent 4 over a field of characteristic 2 of cardinality at least 4.

Keywords

Primary: 16U6017B60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 1 , 01 March 1997 , pp. 103 - 107
Copyright
Copyright © Canadian Mathematical Society 1997

References

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