Geodesic
On a method of constructing $C$-groups
Izvestiya. Mathematics, Tome 59 (1995) no. 4, pp. 765-783 
Yu. V. Kuz'min. On a method of constructing $C$-groups. Izvestiya. Mathematics, Tome 59 (1995) no. 4, pp. 765-783. http://geodesic.mathdoc.fr/item/IM2_1995_59_4_a5/
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     title = {On a~method of constructing $C$-groups},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The groups in question are the metabelian groups which can be given by defining relations $x^{-1}_\alpha x_\beta x_\alpha=x_\gamma$. We give a characterization and constructions of such groups under the assumption that all generators are conjugate.

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