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Journal of the London Mathematical Society 2003 68(2):371-382; doi:10.1112/S0024610703004319
© 2003 by London Mathematical Society
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© The London Mathematical Society

A Non-Finitely Based Variety of Centre-by-Abelian-by-Nilpotent Groups of Exponent 8

Alexei N. Krasilnikov

Department of Mathematics, University of Brasília 70910-900 Brasília-DF, Brazil, alexei{at}mat.unb.br

Received 28 May 2002. Revision received 26 November 2002.

The first example of a non-finitely based variety of centre-by-abelian-by-nilpotent groups was found in 1995. This example has an infinite exponent but it can be seen that the method used to construct it also gives a variety that has an exponent of 128. Later it was proved that there exists a variety with similar properties but with an exponent of 32. The paper constructs a non-finitely based variety of centre-by-abelian-by-nilpotent groups which has an exponent of 8.


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