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Methods Funct. Anal. Topology 26 (2020), no. 1, 88-96
This paper is devoted to a study of special subgroups of automorphism groups of Kronrod-Reeb graphs of Morse functions on $2$-torus $T^2$ which arise from actions of diffeomorphisms preserving a given Morse function on $T^2$. In this paper we give a full description of such classes of groups.