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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: [email protected].
Akbar Rhemtulla
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1 E-mail address: [email protected].
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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

REFERENCES

1.Allambergenov, Kh. S. and Romankov, V. A., Product of commutators in groups, Dokl. Akad. Nauk. UzSSR (1984), No. 4, 14–15 (Russian).Google Scholar
2.Bavard, C. and Meigniez, G., Commutateurs dans les groupes metabeliens, lndag. Math. N.S. 3 (2) (1992), 129–135.CrossRefGoogle Scholar
3.Hartley, B., Subgroups of finite index in profinite groups, Math Z. 168 (1979), 71–76.CrossRefGoogle Scholar
4.Stroud, P., Ph.D. Thesis (Cambridge, 1966).Google Scholar