Extensions and automorphisms of Rota-Baxter groups.

The notion of Rota-Baxter groups was recently introduced by Guo, Lang and Sheng [19] in the geometric study of Rota-Baxter Lie algebras. They are closely related to skew braces as observed by Bardakov and Gubarev. In this paper, we study extensions of Rota-Baxter groups by constructing suitable cohomology theories. Among others, we find relations with the extensions of skew braces. Given an extension of Rota-Baxter groups, we also construct a short exact sequence connecting various automorphism groups, which generalizes the Wells short exact sequence. [ABSTRACT FROM AUTHOR]