# On F-injectors of Fitting set of a finite group

## TL;DR

This paper investigates the existence, conjugacy, and structure of F-injectors within generalized pi-soluble groups, extending understanding of their internal subgroup configurations.

## Contribution

It establishes the existence and conjugacy of F-injectors in generalized pi-soluble groups and describes their structural properties.

## Key findings

- Proved the existence of F-injectors in the specified groups.
- Established the conjugacy of F-injectors.
- Provided a structural description of the injectors.

## Abstract

Let $G$ be some generalized $\pi$-soluble groups and ${\cal F}$ be a Fitting set of $G$. In this paper, we prove the existence and conjugacy of ${\cal F}$-injectors of $G$, and give a description of the structure of the injectors.