Geodesic
Metabelian pro-$p$-groups with a single relation
Algebra i logika, Tome 59 (2020) no. 1, pp. 116-122

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It is proved that there exist uncountably many nonisomorphic pro-$p$-groups admitting presentations with two generating elements and one defining relation in the variety of metabelian pro-$p$-groups. Also we give information on pro-$p$-groups with a single relation in varieties of nilpotent pro-$p$-groups.
Mots-clés : pro-$p$-group
Keywords: variety of metabelian pro-$p$-groups, variety of nilpotent pro-$p$-groups. 
@article{AL_2020_59_1_a6,
     author = {N. S. Romanovskii},
     title = {Metabelian pro-$p$-groups with a single relation},
     journal = {Algebra i logika},
     pages = {116--122},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_1_a6/}
}
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N. S. Romanovskii. Metabelian pro-$p$-groups with a single relation. Algebra i logika, Tome 59 (2020) no. 1, pp. 116-122. http://geodesic.mathdoc.fr/item/AL_2020_59_1_a6/