The congruence subgroup problem for the free metabelian group on generators

  • David El-Chai Ben-Ezra

    The Hebrew University of Jerusalem, Israel
The congruence subgroup problem for the free metabelian group on $n\geq4$ generators cover
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Abstract

The congruence subgroup problem for a finitely generated group asks whether the map is injective, or more generally, what is its kernel ? Here denotes the profinite completion of . It is well known that for finitely generated free abelian groups for every , but , where is the free profinite group on countably many generators.

Considering, the free metabelian group on generators, it was also proven that and . In this paper we prove that for is abelian. So, while the dichotomy in the abelian case is between and , in the metabelian case it is between and .

Cite this article

David El-Chai Ben-Ezra, The congruence subgroup problem for the free metabelian group on generators. Groups Geom. Dyn. 14 (2020), no. 3, pp. 729–764

DOI 10.4171/GGD/561