Groups, Geometry, and Dynamics


Full-Text PDF (182 KB) | Metadata | Table of Contents | GGD summary
Volume 10, Issue 2, 2016, pp. 583–599
DOI: 10.4171/GGD/357

Published online: 2016-06-09

The congruence subgroup problem for the free metabelian group on two generators

David El-Chai Ben-Ezra[1]

(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