# P-stable linear representation

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.