Confusion with Lang's proof of Sylow Theorem
Let’s see. If there’s no element of order $p$, mustn’t the exponent be prime to $p$? Granting that, let the exponent be $m$, but then $np | m^r$, looks like a contradiction.
Let’s see. If there’s no element of order $p$, mustn’t the exponent be prime to $p$? Granting that, let the exponent be $m$, but then $np | m^r$, looks like a contradiction.