Bruno R. Ramos

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math.KT2026

On the abelianization of congruence subgroups of $SL_{2}$ over $S$ -integers

Pedro H. Amorim, Isadora V. Picinini, Bruno R. Ramos +1

In this work, we compute the first integral homology, or abelianization, of the congruence subgroups $Γ (A, m_{A}), Γ_{1} (A, m_{A})$ , and $Γ_{0} (A, m_{A})$ fo…

math.KT2025

The second integral homology of $SL_{2} (Z [1/ n])$

Behrooz Mirzaii, Bruno Reis Ramos, Thiago Verissimo

In this article, we explore the second integral homology, or Schur multiplier, of the special linear group $SL_{2} (Z [1/ n])$ for a positive integer $n$ . We definitively…

On the abelianization of congruence subgroups of SL2​ over S-integers

The second integral homology of SL2​(Z[1/n])

On the abelianization of congruence subgroups of $SL_{2}$ over $S$ -integers

The second integral homology of $SL_{2} (Z [1/ n])$