2
$\begingroup$

Is $U(2^{n})$ isomorphic to $\mathbb{Z_{2}} \bigoplus \mathbb{Z_{2^{n-2}}}$ if $n\geq3$?

And is $U(p^{n})$ isomorphic to $\mathbb{Z_{p^{n}-p^{n-1}}}$ where $p$ an odd prime?

I'm really wondering about its proof.

It's not my homework. I used this fact when doing my homework. I don't have to prove this fact for my homework. This question is just for curiosity.

  • 1
    Related to and possible duplicate of http://math.stackexchange.com/questions/42755/order-of-cyclic-groups.2011-08-16
  • 0
    @Kim Hee yeon: I have merged your unregistered account with your registered account ([this one](http://math.stackexchange.com/users/14654/)). If you encounter any further trouble logging in, please let one of the moderators know (via a post on [meta](http://meta.math.stackexchange.com/), or via a comment)2011-08-16

1 Answers 1