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Characteristic subgroups of relatively free groups

Published online by Cambridge University Press:  17 April 2009

Roger M. Bryant
Roger M. Bryant
Affiliation:
Department of Mathematics, University of Manchester Institute of Science and Technology, Manchester M60 1QD, United Kingdom
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Abstract

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A simple new proof is given of a result of Vaughan-Lee which implies that if G is a relatively free nilpotent group of finite rank k and nilpotency class c with c < k then the characteristic subgroups of G are all fully invariant. It is proved that the condition c < k can be weakened to c < k + p − 2 when G has p–power exponent for some prime p. On the other hand it is shown that for each prime p there is a 2-generator relatively free p-group G which is nilpotent of class 2p such that the centre of G is not fully invariant.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 3 , December 1992 , pp. 497 - 507
Copyright
Copyright © Australian Mathematical Society 1992

References

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