### Sylow p-Subgroups, Conjugacy and Abelian Groups

A) Let G be a group of order 203. Prove that if H is normal subgroup of order 7 in G then H<=Z(G). Deduce that G is abelian in this case. b)Let P be a normal Sylow p-subgroup of G and let H be any subgroup of G. Prove that P intersect H is the unique Sylow p-subgroup of H. c)Let P be in Syl_p(G) and assume N is a normal su