ALGEBRAIC SETS IN A FINITELY GENERATED 2-STEP SOLVABLE RIGID PRO-p-GROUP

作者：Romanovskii N S^*

来源：Algebra and Logic, 2016, 54(6): 478-488.

DOI：10.1007/s10469-016-9367-8

• finitely generated 2-step solvable rigid pro-p-group
• algebraic set

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 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.

• 出版日期2016-1