Assignment:
Let G be a nonabelian group and Z(G) be its center. Show that the factor group G/Z(G) is not a cyclic group.
We know if G is abelian, Z(G)=G. But now if it is not abelian, can we simply say because G is not cyclic, then any factor group will not be cyclic either? or is there more to it?
Provide complete and step by step solution for the question and show calculations and use formulas.