Suppose |G| = 16 and Z(G) contains an element of order 4. What is the isomorphism type of G/Z(G)? I am sure that you have to use the fundamental theorem of abelian groups and the G/Z(G) theorem but I am not sure how to apply these to the problem?
Suppose |G| = 16 and Z(G) contains an element of order 4. What is the isomorphism type of G/Z(G)? I am sure that you have to use the fundamental theorem of abelian groups and the G/Z(G) theorem but I am not sure how to apply these to the problem?
SO .
Now, it can't be since then is cyclic non-trivial, which is impossible (this itself is a nice problem!), so it must be
either is abelian, or else since, as mentioned above, this factor