Hey there, i have a question on the center of a group.

The centre Z(G) of a group G is defined by

(i) Show that Z(G) is normal subgroup of G

(ii) By considering the Class Equation of G acting on itself by conjugation show that if ( p prime) then

(iii) If G is non abelian show that G/Z(G) is not cyclic.

(iv) Decude that any group of order is abelian.

(V) Deduce that a gorup of oder is isomorhpic either to or to

any hints would be greatly appreicated and ill atempt the question once i have a clear idea of how to do them. consequently, i will post them online once i have worked them out. cheers guyz