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

1. Mar 10, 2005

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

2. Mar 10, 2005

Galileo

Isomorphic to what?

3. Mar 10, 2005

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)

Last edited: Mar 10, 2005
4. Mar 10, 2005

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)

Last edited: Mar 10, 2005