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Concerning nilpotent wreath products

Published online by Cambridge University Press:  24 October 2008

Hans Liebeck
Hans Liebeck
Affiliation:
Department of MathematicsUniversity of KeeleStaffordshire
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Extract

In a recent paper, (2), Baumslag showed that a wreath product of A by B is nilpotent if and only if A and B are nilpotent p-groups for the same prime p, with A of finite exponent and B finite. We shall calculate the (nilpotency) class of such groups when A and B are Abelian. This provides a lower bound for the class in the general case. We give a simple construction for a set of non-nilpotent metabelian groups which satisfy a finite Engel condition. With Engel class defined by Definition 6·1, we show that there are nilpotent groups of arbitrarily large nilpotency class for which the nilpotency class is equal to the Engel class.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 3 , July 1962 , pp. 443 - 451
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

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