Finite Localities I

TL;DR

This paper explores the structure of partial groups, objective partial groups, and finite localities, focusing on the properties and quotient constructions involving partial normal subgroups.

Contribution

It introduces new insights into the quotient of a locality by a partial normal subgroup within the framework of partial groups.

Findings

Characterization of quotient structures of localities

Properties of partial normal subgroups in localities

New theoretical results on partial groups and localities

Abstract

This paper concerns partial groups, objective partial groups, and (finite) localities, with special attention given to the quotient of a locality by a partial normal subgroup.