Primitivity in the free groups of the variety UmUn |
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| Authors: | C K Gupta E I Timoshenko |
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| Institution: | 1. Department of Mathematics , University of Manitoba , Manitoba R3T 2N2, Winnipeg, Canada;2. Academy of Civil Engineering , Novosibirsk, 63008, Russia |
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| Abstract: | For each m,n >= 0, let Gm,n denote the free group of rank r in the variety UmUn. The main results in this paper are: (i) a necessary and sufficient condition for a system of r elements {v1,…, vr} to form a basis of Gm,ni (ii) necessary and sufficient conditions for a system of l elements {v1,…, vl}, l <= r, to be included in a basis of Gm,0. In particular, (i), (ii) yield corresponding results for the free metabelian group of rank r. |
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