On injectors of Hartley set of a finite group

TL;DR

This paper investigates the existence, conjugacy, and structure of H-injectors within finite groups, providing new insights and generalizations related to Hartley sets.

Contribution

It establishes the existence and conjugacy of H-injectors in finite groups and describes their structure, extending known results in group theory.

Findings

Proves the existence of H-injectors in finite groups.

Shows conjugacy of H-injectors.

Describes the structural properties of H-injectors.

Abstract

Let G be a group and H be a Hartley set of G. In this paper, we prove the existence and conjugacy of H-injectors of G and describe the structure of the injectors. As application, some known results are directly followed.