Let be a prime, a finite group, and a -Sylow subgroup of . Let be any subgroup of which contains . Prove that (mod ). (Hint: look carefully at Sylow's Theorems.)
Let be a prime, a finite group, and a -Sylow subgroup of . Let be any subgroup of which contains . Prove that (mod ). (Hint: look carefully at Sylow's Theorems.)
The number of conjugates to is .
By Sylow's third theorem .
But since divides it means also.