A Wells-like exact sequence for abelian extensions of relative Rota--Baxter groups

Relative Rota–Baxter groups, a generalization of Rota–Baxter groups, are closely connected to skew left braces, which play a fundamental role in understanding non-degenerate set-theoretical solutions to the Yang-Baxter equation. In this paper, we explore the inducibility problem for automorphisms of abelian extensions of relative Rota–Baxter groups. This problem is intricately linked to the recently introduced second cohomology of relative Rota–Baxter groups. Specifically, we prove a Wells-like exact sequence for abelian extensions of relative Rota–Baxter groups. The sequence establishes a connection among the group of derivations, certain automorphism group, and the second cohomology of relative Rota–Baxter groups, thereby giving precise structural relationships between these groups.