Generalisations of the tame automorphisms over a domain of positive characteristic

TL;DR

This paper introduces two new generalizations of the tame automorphism subgroup over polynomial rings in positive characteristic and analyzes their structures in two-variable cases.

Contribution

It presents novel generalizations of tame automorphisms and provides detailed structural analysis in the two-variable setting.

Findings

Two new tame subgroup generalizations introduced

Structural properties analyzed for two-variable case

Enhanced understanding of automorphism groups in positive characteristic

Abstract

In this paper, we introduce two generalizations of the tame subgroup of the automorphism group of a polynomial ring over a domain of positive characteristic. We study detailed structures of these new `tame subgroups' in the case of two variables.