Answer Happy

Let G be a non-Abelian group of order 8. Let Z = Z(G).
(a) Prove that |Z|= 2.
(b) Prove that each nonidentity element of G/Z has order 2.
(c) Prove that there is a ∈G of order 4 and prove that N = 〈a〉
is a normal subgroup of G. Furthermore, prove that a^2 is the
non-identity element of Z.
Let G be a non-Abelian group of order 8. Let 2 = 2(G). (a) Prove that 12 = 2. (b) Prove that each nonidentity element of G/Z has order 2. (c) Prove that there is a EG of order 1 and prove that N = (a) is a normal subgroup of G. Furthermore, prove that ois the non-identity element of Z.