The group of generalized transposition classes and its automorphisms

In this paper, we introduce the group $ECT(\mathbb{Z})$ generated by generalized class transpositions. It is shown that the S. Kohl automorphism of the group $CT(\mathbb{Z})$ is induced by an inner automorphism of the group $Sym(\mathbb{Z})$ and can be represented as a product of two automorphisms of the group $Sym(\mathbb{Z})$~--- a shift by 1 and a mirroring with respect to 0. We find formulas for the action of these automorphisms on generators of the group $ECT(\mathbb{Z})$$.

УДК 512.54, 512.544.4

Keywords: substitution, class transposition, involution, automorphism, Collatz problem.