s are A 1 Sylow's theorem I gives that for any group that all its Sylow p-subgroup. conjugate. Prove the following: lad for a G with group normal subgroup A Let Ap be sy low p-subgroup of A then G= A Nl'Ap] where NCAP the normalizer of Ap in G. (b) For a group G, with a subgroup H which containS NIGp ) the normalizer of a Sylow p-subgroup sp of G. Then prove N(H)= H. a s are A 1 Sylow's theorem I gives that for any group that all its Sylow p-subgroup. conjugate. Prove the following: lad for a G with group normal subgroup A Let Ap be sy low p-subgroup of A then G= A Nl'Ap] where NCAP the normalizer of Ap in G. (b) For a group G, with a subgroup H which containS NIGp ) the normalizer of a Sylow p-subgroup sp of G. Then prove N(H)= H. a