P-stable linear representation

Definition
Let $$G$$ be a finite group and $$p$$ be an odd prime number. Suppose $$\rho:G \to GL(V)$$ is a linear representation of $$G$$ over a finite field of characteristic $$p$$. We say that $$\rho$$ is $$p$$-stable if for no non-identity $$p$$-element $$g$$ of $$G$$ (i.e., an element whose order is a power of $$p$$) does $$\rho(g)$$ satisfy a quadratic minimal polynomial.