Generating Elements for Groups of the Form F/R' |
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| Authors: | C K Gupta E I Timoshenko |
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| Institution: | (1) Department of Mathematics, University of Manitoba, Winnipeg, R3T 2N2, Canada;(2) Nikitina 62-29, Novosibirsk, 630008 |
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| Abstract: | Necessary and sufficient conditions are specified for a group of a specified type to be generated by its given elements (F is a free product). Using these conditions (and relying essentially on the Shmel'kin embedding), we establish the criterion of being primitive for metabelian products of Abelian groups. A result by Birman and the primitivity criterion for free metabelian groups are generalized. |
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