Let G be a group such that every subgroup of G is subnormal. Suppose that there exists N normal subgroup of G such that Z(N) is nontrivial and G/N is cyclic. Prove that Z(G) is nontrivial. (Z(G) denotes the center of G).Note: A subgroup H of G is subnormal if there exist subgroups H1,H2,…,Hm=G of G such that H⊲H1⊲H2⊲…⊲Hm=G (⊲ denotes normal subgroup). group theoryabstract algebrasuperior algebrasuperior algebra unsolved