J. Austral. Math. Soc.  73 (2002), 55-84
Metanilpotent varieties of groups

R. M. Bryant
  UMIST
  PO Box 88
  Manchester M60 1QD
  UK
  bryant@umist.ac.uk
and
A. N. Krasil'nikov
  Moscow Pedagogical State University
  14 Krasnoprudnaya ul.
  Moscow 107140
  Russia
  Current address:
  University of Brasilia
  70910-900 Brasilia-DF
  Brazil
  alexei@mat.unb.br


Abstract
For each positive integer  n  let ${\bf N}_{2,n}$ denote the variety of all groups which are nilpotent of class at most  2  and which have exponent dividing   n. For positive integers   m  and   n, let ${\bf N}_{2,m}{\bf N}_{2,n}$ denote the variety of all groups which have a normal subgroup in ${\bf N}_{2,m}$ with factor group in ${\bf N}_{2,n}$. It is shown that if $G \in {\bf N}_{2,m}{\bf N}_{2,n}$, where   m  and   n  are coprime, then $G$ has a finite basis for its identities.
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