# Chapter 11

*Exercise 1. *This software
lists the isomorphism classes of all finite Abelian groups of order
*n*.
Assume that *n* < 1,000,000. Run your program for *n =* 16,
24, 512, 2048, 441000, and 999999.

*Exercise 2. *This software
determines how many integers in a given interval are the order of exactly
one Abelian group, of exactly two Abelian groups, and so on, up to exactly
nine Abelian groups. Run your program for the integers up to 1000.
Then from 10001 to 11000. Then choose your own interval of 1000 consecutive
integers. Is there much difference in the results?

*Exercise 3. *This software
expresses *U*-groups
as internal direct product of subgroups
*H*_{1} X
H_{2} X ... X
H_{t}, where
|H_{i}| divides
*|H*_{i -1|} .
Run your
program for the groups *U*(32),
*U*(80), and *U*(65).