Is this correct: "any two Sylow p-subgroups of $GL_2(p)$ generate $SL_2(p)$"?
I see this in the book "The Classification of the Finite Simple Groups, Number 5" (p.40). But I don't know how to prove it.
I know that the order of $GL_2(p)$ is $p(p+1)(p-1)^2$ and the number of Sylow $p$-subgroups of $GL_2(p)$ is $p+1$.