Geodesic
Algebraic sets in a finitely generated rigid $2$-step solvable pro-$p$-group
Algebra i logika, Tome 54 (2015) no. 6, pp. 733-747
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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 torsion-free Abelian, and the subgroup $G_2$ is also Abelian and is torsion-free as a $\mathbb Z_pA$-module, where $\mathbb Z_pA$ is the group algebra of the group $A$ over the ring of $p$-adic integers. For instance, free metabelian pro-$p$-groups of rank $\ge2$ 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 $G$.
Keywords: finitely generated $2$-step solvable rigid pro-$p$-group, algebraic set. 
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     title = {Algebraic sets in a~finitely generated rigid $2$-step solvable pro-$p$-group},
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     url = {http://geodesic.mathdoc.fr/item/AL_2015_54_6_a3/}
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N. S. Romanovskii. Algebraic sets in a finitely generated rigid $2$-step solvable pro-$p$-group. Algebra i logika, Tome 54 (2015) no. 6, pp. 733-747. http://geodesic.mathdoc.fr/item/AL_2015_54_6_a3/

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