# On the behavior of $\pi$-submaximal subgroups under homomorphisms

## TL;DR

This paper investigates how $\pi$-submaximal subgroups behave under group homomorphisms by providing specific examples that highlight differences from $\pi$-maximal subgroups.

## Contribution

It offers new insights and explicit examples demonstrating the distinct behavior of $\pi$-submaximal subgroups under homomorphisms.

## Key findings

- Examples showing divergence in behavior of $\pi$-submaximal subgroups
- Differences between $\pi$-maximal and $\pi$-submaximal subgroups under homomorphisms
- Clarification of subgroup behavior in group theory contexts

## Abstract

We construct examples that show the difference in behavior or $\pi$-maximal and $\pi$-submaximal subgroups under group homomorphisms.