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Bounds for the class of nilpotent wreath products

Published online by Cambridge University Press:  24 October 2008

Teresa Scruton
Teresa Scruton
Affiliation:
University of Sussex
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Extract

Introduction. In his paper ((1)), Baumslag has shown that the wreath product A wr B of a group A by a group B is nilpotent if and only if A is a nilpotent p-group of finite exponent and B is a finite p-group, the prime p being the same for both groups. Liebeck ((3)) has obtained the exact nilpotency class of A wr B when A and B are Abelian. Let A be an Abelian p -group of exponent pn and let B be a direct product of cyclic groups, whose orders are pβ1, …, pβn, with β1 ≤ β2 ≤ … βn. Then A wr B has nilpotency class .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 2 , April 1966 , pp. 165 - 169
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

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