Geodesic
Generating Elements for Groups of the Form $F/R'$
Algebra i logika, Tome 40 (2001) no. 3, pp. 251-261 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: metabelian products of Abelian groups, free metabelian group, generator. 
@article{AL_2001_40_3_a0,
     author = {Ch. K. Gupta and E. I. Timoshenko},
     title = {Generating {Elements} for {Groups} of the {Form} $F/R'$},
     journal = {Algebra i logika},
     pages = {251--261},
     year = {2001},
     volume = {40},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2001_40_3_a0/}
}
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Ch. K. Gupta; E. I. Timoshenko. Generating Elements for Groups of the Form $F/R'$. Algebra i logika, Tome 40 (2001) no. 3, pp. 251-261. http://geodesic.mathdoc.fr/item/AL_2001_40_3_a0/