Large Sets in Countable Amenable Group and its Applications

TL;DR

This paper extends the concept of D-sets within countable amenable groups, explores their relation to weak mixing in group actions, and establishes equivalences of *-notions in polynomial groups over finite fields.

Contribution

It introduces an extension of D-sets in countable amenable groups and investigates their connections to weak mixing and *-notions in polynomial groups over finite fields.

Findings

Extended D-sets in countable amenable groups.

Connected D-sets with weak mixing properties.

Proved equivalence of *-notions in polynomial groups over finite fields.

Abstract

In the present paper our main objective is to extend the notion of $D$-sets in countable amenable groups and to discuss its connection with weak mixing for amenable group actions. Further we prove that *-notions are equivalent in the countable amenable group of polynomials generated by finite fields.