A 2-step solvable pro-p-group G is said to be rigid if it contains a normal series of the form G = G 1 > G 2 > G 3 = 1 such that the factor group A = G/G 2 is torsionfree Abelian, and the subgroup G 2 is also Abelian and is torsion-free as a ℤ p A-module, where ℤ p A is the group algebra of the group A over the ring of p-adic integers. For instance, free metabelian pro-p-groups of rank ≥ 2 are rigid. We give a description of algebraic sets in an arbitrary finitely generated 2-step solvable rigid pro-p-group G, i.e., sets defined by systems of equations in one variable with coefficients in G.
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(N. S. Romanovskii) Supported by RFBR, project No. 15-01-01485.
Translated from Algebra i Logika, Vol. 54, No. 6, pp. 733–747, November-December, 2015.
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Romanovskii, N.S. Algebraic Sets in a Finitely Generated 2-Step Solvable Rigid Pro-p-Group. Algebra Logic 54, 478–488 (2016). https://doi.org/10.1007/s10469-016-9367-8
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DOI: https://doi.org/10.1007/s10469-016-9367-8