Solitary quotients of finite groups

TL;DR

This paper introduces the concept of solitary quotients in finite groups, exploring their lattice structure and providing detailed descriptions for specific classes of finite groups.

Contribution

It defines and studies the lattice of normal subgroups that determine solitary quotients, linking it to solitary subgroups and offering explicit descriptions for certain finite groups.

Findings

Lattice of solitary quotients is closely connected to solitary subgroups.

Explicit descriptions provided for some classes of finite groups.

New framework for analyzing normal subgroups related to solitary quotients.

Abstract

In this paper we introduce and study the lattice of normal subgroups of a group $G$ that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of $G$ (see \cite{5}). A precise description of this lattice is given for some particular classes of finite groups.