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)
View other properties of finite groups OR View all group properties

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.

Relation with other properties

Stronger properties

Weaker properties