University of Isfahan International Journal of Group Theory 2251-7650 15 4 2026 02 01 On Rota--Baxter operators on finite simple groups of Lie type 215 225 30198 10.22108/ijgt.2026.147698.2003 EN Alexey Galt Novosibirsk State University, Pirogova str. 1, P.O.Box 630090, Novosibirsk, Russia Vsevolod Gubarev Novosibirsk State University, Pirogova str. 1, P.O.Box 630090, Novosibirsk, Russia Journal Article 2025 12 05 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.<br /> <br />Now we describe Rota--Baxter operators on finite simple exceptional groups of Lie type and projective special linear groups of degree two. https://ijgt.ui.ac.ir/article_30198_f2ea30188dc62982b146b62fd948eac5.pdf