On Rota--Baxter operators on finite simple groups of Lie type

Rota–Baxter operators on groups were introduced by L. Guo, H. Lang, Yu. Sheng in 2020. In 2023, V. Bardakov and the second author showed that all Rota–Baxter operators on simple sporadic groups are splitting, i.,e. they correspond to exact factorizations of groups. In 2024, the authors of the current paper described all non-splitting Rota–Baxter operators on alternating groups. Now we describe Rota–Baxter operators on finite simple exceptional groups of Lie type and projective special linear groups of degree two.