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On nilpotent 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

1. Introduction. 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 for the same prime p (Baumslag (1)). When A is an Abelian p-group of exponent pk, and B is the direct product of cyclic groups of orders pβ1, …, pβn and β1 ≥ β2 ≥ …, ≥ βn, then Liebeck has shown that the nilpotency class c of A wr B is

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 1 - 15
Copyright
Copyright © Cambridge Philosophical Society 1970

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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)Liebeck, H.Concerning nilpotent wreath products. Proc. Cambridge Philos. Soc. 58 (1962), 443–451.CrossRefGoogle Scholar
(3)Meldrum, J. D. P.Central series in wreath products. Proc. Cambridge Philos. Soc. 63 (1967), 551–567.CrossRefGoogle Scholar
(4)Neumann, B. H., Neumann, H. and Neumann, P. M.Wreath products and varieties of groups. Math. Z. 80 (1962), 44–62.CrossRefGoogle Scholar
(5)Scruton, T.Bounds for the class of nilpotent wreath products. Proc. Cambridge Philos. Soc. 62 (1966), 165–169.CrossRefGoogle Scholar