Abstract
The theory of Rota–Baxter operators on rings and algebras has been developed since 1960. In 2020, the notion of Rota–Baxter operator on a group was defined. Further, it was proved that one may define a skew left brace on any group endowed with a Rota–Baxter operator. Thus, a group endowed with a Rota–Baxter operator gives rise to a set-theoretical solution to the Yang–Baxter equation. 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.
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