  Theory of Rota-Baxter operators on rings and algebras has been developed
since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined
the notion of Rota-Baxter operator on a group. We provide some general
constructions of Rota-Baxter operators on a group. Given a map on a group, we
study its extensions to a Rota-Baxter operator. We state the connection between
Rota-Baxter operators on a group and Rota-Baxter operators on an associated Lie
ring. We describe Rota-Baxter operators on sporadic simple groups.
