# Linearly primitive group

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This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)
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## Definition

### Symbol-free definition

A finite group is said to be linearly primitive if it has a faithful irreducible representation over an algebraically closed field of characteristic zero (or equivalently, over the algebraic closure of rationals or over the complex numbers).

### Definition with symbols

A group $G$ is said to be linearly primitive if there is a homomorphism $\sigma:G \to GL(V)$ for some vector space $V$ over the complex numbers, such that $V$ has no proper nonzero $G$-invariant subspace.