# Irreducible induction and nilpotent subgroups in finite groups

## TL;DR

This paper proves that if a nilpotent subgroup's character induces an irreducible character in a finite group, then the generalized Fitting subgroup of the group must also be nilpotent, revealing a structural property of such groups.

## Contribution

It establishes a new link between induced characters from nilpotent subgroups and the nilpotency of the generalized Fitting subgroup in finite groups.

## Key findings

- Induction of an irreducible character from a nilpotent subgroup implies the generalized Fitting subgroup is nilpotent.
- Provides a structural criterion for nilpotency in finite groups based on character induction.
- Enhances understanding of the relationship between subgroup properties and the overall group structure.

## Abstract

Suppose that $G$ is a finite group and $H$ is a nilpotent subgroup of $G$. If a character of $H$ induces an irreducible character of $G$, then the generalized Fitting subgroup of $G$ is nilpotent.