On Orbits and Bi-invariant Subsets of Binary $G$-Spaces

TL;DR

This paper investigates the structure of orbits and bi-invariant subsets in binary G-spaces, solving a 2016 problem regarding the distributivity of binary group actions on spaces.

Contribution

It provides a solution to the open problem of distributivity of binary group actions on spaces, advancing the understanding of binary G-spaces.

Findings

Solved the 2016 problem on distributivity of binary G-actions

Characterized bi-invariant subsets in binary G-spaces

Enhanced understanding of orbit structures in binary G-spaces

Abstract

Orbits and bi-invariant subsets of binary $G$-spaces are studied. The problem of the distributivity of a binary action of a group $G$ on a space $X$, which was posed in 2016 by one of the authors, is solved.