It is known that the intersectionn of kernels of all ireductibile representations of a finite group in charcteristic zero is the trivial group.

In caracteristic p I have understood that this intersection îs $O_p(G)$, the largest normal p - subgroup of G. In other words, all irreducible represntations of G are coming from the quotient $G/O_p(G)$.

I have some dificulties to proove this similar result in characteristic p dividing the order of G. Could Simeone please give a reference for this result? Or shortly explain the argument to me. My intuition is that this is not so difficult.