Groups, Geometry, and Dynamics
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Published online: 2016-06-09
The congruence subgroup problem for the free metabelian group on two generatorsDavid El-Chai Ben-Ezra (1) The Hebrew University of Jerusalem, Israel
In this paper we describe the profinite completion of the free solvable group on $m$ generators of solvability length $r \geq 1$. Then, we show that for $m = r = 2$, the free metabelian group on two generators does not have the Congruence Subgroup Property.
Keywords: Congruence subgroup problem, profinite completion, free metabelian group, free solvable group
Ben-Ezra David El-Chai: The congruence subgroup problem for the free metabelian group on two generators. Groups Geom. Dyn. 10 (2016), 583-599. doi: 10.4171/GGD/357