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.
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D. Kochloukova, “Uncountably many non-commensurable pro-p-groups of homological type FPk but not FPk+1,” Int. J. Algebra Comput., 29, No. 7, 1219-1234 (2019).
L. Ribes and P. Zalesskii, Profinite Groups, Ergebn. Math. Grenzg. 3, 40, Springer, Berlin (2000).
J. S. Wilson, Profinite Groups, London Math. Soc. Mon., New Ser., 19, Clarendon, Oxford (1998).
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Supported by SB RAS Fundamental Research Program I.1.1, project No. 0314-2019-0001.
Translated from Algebra i Logika, Vol. 59, No. 1, pp. 116-122, January-February, 2020.
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Romanovskii, N.S. Metabelian Pro-p-Groups with a Single Relation. Algebra Logic 59, 82–86 (2020). https://doi.org/10.1007/s10469-020-09580-1
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DOI: https://doi.org/10.1007/s10469-020-09580-1