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Bounds on the Engel class of some group extensions

Published online by Cambridge University Press:  24 October 2008

David Shield
David Shield
Affiliation:
Australian National University
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Abstract

In this paper upper bounds on the Engel length of a group G of prime-power exponent are obtained, under varying conditions on a normal subgroup H and the quotient G/H. Examples are constructed to show that the bounds are best possible when the nilpotency class of H is less than the relevant prime.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 179 - 188
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Bachmuth, S. and Hughes, I.Applications of a theorem of Magnus. Arch. Math. 17 (1966), 380–382.CrossRefGoogle Scholar
(2)Baumslag, G.Wreath products and p-groups. Proc. Cambridge Philos. Soc. 55 (1959), 224–231.CrossRefGoogle Scholar
(3)Huppert, B.Endliche Gruppen I. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen (Springer-Verlag; Berlin, Heidelberg, New York, 1967).Google Scholar
(4)Liebeck, H.Concerning nilpotent wreath products. Proc. Cambridge Philos. Soc. 58 (1962), 443–451.CrossRefGoogle Scholar
(5)Neumann, Hanna. Varieties of Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete (Springer-Verlag; Berlin, Heidelberg, New York, 1967).Google Scholar
(6)Shield, D.Nilpotency and related properties of group extensions. Bull. Austral. Math. Soc. 4 (1971), 145–154.CrossRefGoogle Scholar