Let

P

be a finite p-group and let

N

be a nontrivial normal subgroup of

G

. Show that

N\\\\cap Zz(G)!=1

.\ Further conclude that if

N

has order

p

, then

N

.

Let P be a finite p-group and let. N be a nontrivial normal subgroup of G. Show that NZz(G)=1. Further conclude that if N has order p, then NZ(G)