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Chains of Varieties

Published online by Cambridge University Press:  20 November 2018

Narain Gupta ,
Frank Levin  and
Akbar Rhemtulla
Narain Gupta
Affiliation:
University of Manitoba, Winnipeg, Manitoba
Frank Levin
Affiliation:
Rutgers, The State University, New Brunswick, New Jersey
Akbar Rhemtulla
Affiliation:
University of Alberta, Edmonton, Alberta
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Summary

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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
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 190 - 206
Copyright
Copyright © Canadian Mathematical Society 1974

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