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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

(1)Baumslag, G.Wreath products and p-groups. Proc. Cambridge Philos. Soc. 55 (1959), 224–231.CrossRefGoogle Scholar
(2)Gruenberg, K. W.Residual properties of infinite soluble groups. Proc. London Math. Soc. (3) 7 (1957), 29–62.CrossRefGoogle Scholar
(3)Liebeck, H.Concerning nilpotent wreath products. Proc. Cambridge Philos. Soc. 58 (1962), 443–451.CrossRefGoogle Scholar
(4)Meldrum, J. D. P.On nilpotent wreath products. (Submitted to Proc. Cambridge Philos. Soc.)Google Scholar
(5)Neumann, B. H., Neumann, Hanna and Neumann, P. M.Wreath products and varieties of groups. Math. Z. 80 (1962), 44–62.CrossRefGoogle Scholar