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Chains of Varieties
Published online by Cambridge University Press: 20 November 2018
Summary
If is a variety of groups that can be denned by n-variable laws and
(m) is the variety all of whose m-generator groups are in
then there corresponds the chain:
(1) ≧
(2) ≧ . . . ≧
(n) =
. In this paper such chains are investigated to determine which of the inclusions are proper for certain varieties
. In particular the inclusions are shown to be all proper for the varieties
where
is the variety of nilpotent-of-class-c groups,
is the abelian variety and
is the variety of centre-bymetabelian groups. For
the inclusions are likewise proper but for
the corresponding chain is:
- Type
- Research Article
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- Copyright © Canadian Mathematical Society 1974
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