Generating groups of nilpotent varieties
- 1 August 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 3 (2) , 145-154
- https://doi.org/10.1017/s0004972700045809
Abstract
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).Keywords
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- Generating groups of nilpotent varietiesBulletin of the American Mathematical Society, 1968
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