Partial groups as partial groups

TL;DR

This paper explores the concept of partial groups, demonstrating that many binary partial groups in literature can be viewed as partial groups in Chermak's sense, and identifies the largest class of such objects.

Contribution

It clarifies the relationship between binary partial groups and Chermak's partial groups, and characterizes the largest class of these objects.

Findings

Many binary partial groups can be regarded as Chermak's partial groups

Identification of the largest class of such objects

Provides a unifying perspective on partial groups

Abstract

There are many examples of `binary' partial groups in the literature: sets equipped an identity and a partially-defined binary operation, such that each element admits an inverse. We show that many of these may be regarded as partial groups in the sense of Chermak, and single out the largest class of such objects.