Standard Frobenius endomorphism

Definition
Let $$G$$ be a linear algebraic group over a field of positive characteristic $$p$$. A standard Frobenius endomorphism of $$G$$ is an endomorphism of $$G$$ arising as the restriction to $$G$$ of a standard Frobenius endomorphism of the group $$GL_n(k)$$ in which $$G$$ is embedded. Here, a standard Frobenius endomorphism of $$GL_n(k)$$ is defined as an endomorphism that, for some suitable choice of basis, can be expressed as a map sending each matrix entry to its $$q^{th}$$ power (where $$q$$ is a power of $$p$$).

Weaker properties

 * Frobenius endomorphism is an endomorphism such that some power of it is a standard Frobenius endomorphism
 * Injective endomorphism