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Generating groups of nilpotent varieties

Published online by Cambridge University Press:  17 April 2009

M. R. Vaughan-Lee
M. R. Vaughan-Lee
Affiliation:
Vanderbilt University, Nashville, Tennessee, USA.
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Abstract

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If is a variety of groups which are nilpotent of class c then is generated by its free group of rank c. It is proved that under certain general conditions cannot be generated by its free group of rank c - 2, and that under certain other conditions is generated by its free group of rank c - 1. It follows from these results that if is the variety of all groups which are nilpotent of class c, then the least value of k such that the free group of of rank k generates is c - 1. This extends known results of L.G. Kovács, M.F. Newman, P.P. Pentony (1969) and F. Levin (1970).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 2 , October 1970 , pp. 145 - 154
Copyright
Copyright © Australian Mathematical Society 1970

References

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