Rota---Baxter operators on extraspecial groups

Abstract: Theory of Rota--Baxter operators on rings and algebras has been developed since 1960. In 2021, L. Guo, H. Lang, Y. Sheng have defined the notion of Rota---Baxter operator on a group. We classify all Rota---Baxter operators on the finite Heisenberg group and the extraspecial group of order $p<sup>3$. We also investigate an analogue of the spectral property for Rota---Baxter operators on algebras.