Homework answers / question archive / Let G be a nonabelian group and Z(G) be its center

Let G be a nonabelian group and Z(G) be its center

Math

Share With

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?