# Minimally irreducible linear representation

From Groupprops

*This article describes a property to be evaluated for a linear representation of a group, i.e. a homomorphism from the group to the general linear group of a vector space over a field*

## Definition

A finite-dimensional linear representation of a group is said to be **minimally irreducible** if its restriction to any proper subgroup is reducible.

It turns out that the image of a group under a minimally irreducible linear representation must be a finite group.