Find all nonisomorphic abelian gps

[mclove]

Homework Statement

- List all nonisomorphic abelian groups of order 2^3 3^2 5

Homework Equations

The Attempt at a Solution

- Z_2^3 * Z_3^2 * Z_5 = (iso) Z_360.
Z_2^3 * Z_3 * Z_3 * Z_5 = (iso) Z_3 * Z_100
.
.
.
I know ,
but why Z_360 , Z_3 * Z_100 are nonisomorphic to 2^3 3^2 5 ?

 

[Hurkyl]

Because Z_360 == Z_2^3 * Z_3^2 * Z_5, but Z_3 * Z_100 == Z_2^3 * Z_3 * Z_3 * Z_5.

 

[mclove]

Sorry, I don's understand it..
Z_2^3 * Z_3 * Z_3* Z_5 == Z_8 * Z_9 * Z_5 Is this nonabelian groups of order
2^33^25 ??