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Central series in wreath products

Published online by Cambridge University Press:  24 October 2008

J. D. P. Meldrum
J. D. P. Meldrum
Affiliation:
Emmanuel College, Cambridge
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Extract

In this paper we study the structure of the α-central series of the nilpotent wreath product of two Abelian groups, the α-central series being the intersection of the upper central series with the base group. Let C = A wr B, the standard restricted wreath product of A and B. Then Baumslag(1) showed that C is nilpotent if and only if A is a nilpotent p-group of finite exponent and B is a finite p-group for the same prime p. In (5) Liebeck calculated the nilpotency class of the nilpotent wreath product of two Abelian groups. We obtain an expression for an element of the base group to belong to a given term of the upper central series.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 551 - 567
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

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