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In this paper, we study relative Rota-Baxter operators of weight $0$ ongroups and give various examples. In particular, we propose differentapproaches to study Rota-Baxter operators of weight $0$ on groups and Liegroups. We establish various explicit relations among relative Rota-Baxteroperators of weight $0$ on groups, pre-groups, braces, set-theoretic solutionsof the Yang-Baxter equation and $T$-structures.

Relative Rota-Baxter operators of weight 0 on groups, pre-groups, braces, the Yang-Baxter equation and $T$-structures