Normal structure spaces of groups

TL;DR

This paper explores the topological properties of normal subgroups in groups, introducing primitive subgroups and analyzing their separation, compactness, and connectedness, aiming to understand their spectral space characteristics.

Contribution

It introduces primitive subgroups and studies the topological structure of normal subgroups with a hull-kernel topology, expanding the understanding of their spectral properties.

Findings

Analysis of separation axioms and compactness properties

Introduction of primitive subgroups in the topological context

Discussion on spectral spaces among normal subgroups

Abstract

Can we do a topological study of various classes of normal subgroups endowed with a hull-kernel-type topology? In this paper, we have provided an answer to this question. We have introduced as well a new class of normal subgroups called primitive subgroups. Separation axioms, compactness, connectedness, and continuities of these spaces have been studied. We have concluded with the question of determining spectral spaces among them.