# On the problem of existence and conjugacy of injectors of generalized $\pi$-soluble groups

## TL;DR

This paper investigates the existence and conjugacy of injectors in generalized π-soluble groups, providing structural insights and extending classical results to broader classes defined by Hartley functions.

## Contribution

It establishes the existence and conjugacy of injectors in generalized π-soluble groups for Hartley classes, and describes their structure.

## Key findings

- Proves the existence of injectors in generalized π-soluble groups.
- Shows conjugacy of these injectors within the groups.
- Provides a structural description of the injectors.

## Abstract

In this paper, we prove the existence and conjugacy of injectors of a generalized $\pi$-soluble groups for the Hartley class defined by a invariable Hartley function, and give a description of the structure of the injectors.