Abstract:
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 $ECT(\mathbb{Z})$.
Key words:substitution, class transposition, involution, automorphism, Collatz problem.
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