On the Surjectivity of Certain Maps IV: For Congruence Ideal Subgroups of Type $A_k$ and $C_k$

TL;DR

This paper extends surjectivity results for special linear and symplectic groups onto product spaces to certain congruence ideal subgroups, enhancing understanding of their algebraic structure.

Contribution

It introduces new surjectivity results for congruence ideal subgroups of types A_k and C_k, generalizing previous findings for the entire groups.

Findings

Surjectivity established for specific congruence subgroups

Extension of results from full groups to subgroups

Enhanced understanding of algebraic properties of these subgroups

Abstract

For a positive integer $k$, we extend the surjectivity results from special linear groups (Type $A_k$) and symplectic linear groups (Type $C_k$) onto product of generalized projective spaces by associating the rows or columns, to certain congruence ideal subgroups of special linear groups and symplectic linear groups.