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A variety of groups

Published online by Cambridge University Press:  03 February 2005

PAVEL SHUMYATSKY
PAVEL SHUMYATSKY
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900 Brazil. e-mail: pavel@mat.unb.br
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Abstract

The following theorem is proved. For any positive integers $k$ and $n$ there exists $t$ depending only on $k$ and $n$ such that the class of all groups $G$ having $\gamma_k(G)$ locally finite and satisfying the condition that the product of any $t$ commutators of the form $[x_1,x_2,{\dots}\,,x_k]$ is of order dividing $n$ is a variety.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 138 , Issue 1 , January 2005 , pp. 21 - 26
Copyright
2005 Cambridge Philosophical Society

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