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A note on centre-by-finite-exponent varieties of groups

Published online by Cambridge University Press:  09 April 2009

Narain Gupta  and
Akbar Rhemtulla
Narain Gupta
Affiliation:
University of Manitoba
Akbar Rhemtulla
Affiliation:
University of Alberta, Edmonton
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We refer the reader to Hanna Neumann [7] for notation and other undefined terms. Let and denote the varieties of groups defined by the laws (xy)n=xnyn, [x, y]n=1 and [x, yn]respectively, where n is an integer. (n)-groups were termed “n-abelian” by R. Baer [1] and have been a subject matter of investigation by various authors (see [3], [5], [6] and the references therein). Recently KaluŽnin [5] has shown that , thus clarifying the relationship between U(n) and the familiar varieties. From the elementary inequalities(n ≠ 0,1)it is easily deduced that(see for instance [5]). If G = Cm Wr C∞, then cleary but for any Thus and . It is also easy to see that in general (see for instance [6] § 5.1) and we are led to ask

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 1 , February 1970 , pp. 33 - 36
Copyright
Copyright © Australian Mathematical Society 1970

References

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