The behavior of $\pi$-submaximal subgroups under homomorphisms with $\pi$-separable kernels

TL;DR

This paper investigates how $\pi$-submaximal subgroups behave under homomorphisms with $\pi$-separable kernels, highlighting irregularities and advancing the theory of $\mathfrak{X}$-submaximal subgroups.

Contribution

It analyzes the behavior of $\pi$-submaximal subgroups under specific homomorphisms and constructs examples demonstrating irregular behavior, contributing to the inductive theory of $\mathfrak{X}$-submaximal subgroups.

Findings

Identified irregular behavior of $\pi$-submaximal subgroups under certain homomorphisms.

Constructed explicit examples illustrating irregularities.

Extended understanding of the behavior of $\pi$-submaximal subgroups in group theory.

Abstract

We explore the extent to which constructing the inductive theory of $\mathfrak{X}$-submaximal subgroups is possible. To this end, we study the behavior of $\pi$-submaximal subgroups under homomorphisms with $\pi$-separable kernels and construct examples where such behavior is irregular.