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Commutator length of abelian-by-nilpotent groups

Published online by Cambridge University Press:  18 May 2009

Mehri Akhavan-Malayeri  and
Akbar Rhemtulla
Mehri Akhavan-Malayeri
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1 E-mail address: akbar@malindi.math.ualberta.ca.
Akbar Rhemtulla
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1 E-mail address: akbar@malindi.math.ualberta.ca.
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Abstract

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Let G be a group and C = [G, G] be its commutator subgroup. Denote by c(G) the minimal number such that every element of G′ can be expressed as a product of at most c(G) commutators. The exact values of c{G) are computed when G is a free nilpotent group or a free abelian-by-nilpotent group. If G is a free nilpotent group of rank n>2 and class c>2, c(G) = [n/2] if c = 2 and c(G) = n if c>2. If G is a free abelian-by-nilpotent group of rank n > 2 then c(G) = n.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 1 , March 1998 , pp. 117 - 121
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

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