- #1

jstrunk

- 55

- 2

- TL;DR Summary
- I need examples of how to do it

According to the book I am using, one can decompose a finite abelian group uniquely as a direct sum of cyclic groups with prime power orders.

Uniquely meaning that the structures in the group somehow force you to one particular decomposition for any given group.

Unfortunately, the book gives no examples of how to do it and none of the exercises give solutions.

All I want is a pointer to some examples that go through the process slowly at a beginner level.

In particular, no Sylow stuff. At this point in the book we haven't covered Sylow yet so apparently I should be able to do this without it.

I have searched all over the internet and can't find any.

Thanks for your help.

Uniquely meaning that the structures in the group somehow force you to one particular decomposition for any given group.

Unfortunately, the book gives no examples of how to do it and none of the exercises give solutions.

All I want is a pointer to some examples that go through the process slowly at a beginner level.

In particular, no Sylow stuff. At this point in the book we haven't covered Sylow yet so apparently I should be able to do this without it.

I have searched all over the internet and can't find any.

Thanks for your help.