Find:2 Non-isomorphic groups of order n squared. help?

[assman]

Find:2 Non-isomorphic groups of order n squared

i think that Zn X Zn is one.

Can you help me find another.


Thanks

 

[Galileo]

Isomorphic to what?

 

[fourier jr]

nonisomorphic means not isomorphic to each other, doesn't it? like the klein 4-group & Z_4 both have order 2^2 but are nonisomorphic

since K_4 = Z_2 x Z_2 i conjecture off the cuff that the 2 nonisomorphic groups with order n^2 would be Z_n x Z_n and Z_(n^2)

 

[Data]

If you mean non-isomorphic to each other, then you can take Z_(n^2) and Z_n x Z_n, for example (under addition).

In response to the above post: Indeed, those work, since Z_(n^2) is cyclic but Z_n x Z_n is not (you can see this alternatively in terms of vector spaces: dim(Z_(n^2)) = 1 but dim(Z_n x Z_n) = 2)