Linearly primitive group
From Groupprops
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
Contents
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 is said to be linearly primitive if there is a homomorphism
for some vector space
over the complex numbers, such that
has no proper nonzero
-invariant subspace.
Relation with other properties
Stronger properties
Weaker properties
- Cyclic-center group: For full proof, refer: Linearly primitive implies cyclic-center