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Torsion in the additive group of relatively free Lie rings

Published online by Cambridge University Press:  17 April 2009

Vesselin Drensky
Vesselin Drensky
Affiliation:
Institute of Mathematics, Bulgarian Academy of Sciences, 1090 Sofia, P.O. Box 373Bulgaria.
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Abstract

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Let L = L(X) be the free Lie ring of countable rank and let p be prime. Then L(Vp) = L/[(L')p, L] is the relatively free ring for the variety of Lie rings Vp = [Np−1A, E] and Vp is defined by the identity

The purpose of this note is to establish that there exist elements of order p in the additive group of L(Vp). Previously, the existence of p-torsion was proved by Kuz'min for p = 2 only. Similar results were obtained for varieties of groups by Gupta when p = 2 and by Stöhr when p = 3.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 1 , February 1986 , pp. 81 - 87
Copyright
Copyright © Australian Mathematical Society 1986

References

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