2024/01/25 by Pragya Belwal, Belwal, Pragya, Nishant Rathee +1
Mathematics · #16T25 #81R50} #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #[2010]{17B38
paper · pdf · doi:10.48550/arxiv.2401.14058
openalex publication_date 2024/01/25 · openalex created_date 2024/01/27 · openalex updated_date 2026/07/28
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.