On the inheriting of the property $C_\pi$ by some normal subgroups

TL;DR

This paper proves that the Hall property $C_$ is inherited by certain normal subgroups with index coprime to , expanding understanding of subgroup inheritance in group theory.

Contribution

It establishes that normal subgroups with '-index inherit the property $C_$, a significant extension in the theory of Hall properties.

Findings

Normal subgroups with '-index inherit the property $C_$.

The result broadens the class of subgroups known to inherit the $C_$ property.

Provides new insights into the structure of groups with the $C_$ property.

Abstract

In the paper we prove that the Hall property $C_\pi$ is inherited by normal subgroups which index is a $\pi'$-number.