2
$\begingroup$

Is there any natural group structure on the set $I_p = \{x \in \mathbb{Z}[1/p] \mid |x| < p/2\}$?

$\endgroup$
1
  • $\begingroup$ This is a really strange question without any motivation. What could "natural" possibly mean? $\endgroup$ Nov 18, 2009 at 4:30

1 Answer 1

2
$\begingroup$

This set doesn't have a subgroup structure as a subset of the reals, but if p is an odd prime, you can certainly lift the additive group law on Qp/pZp to this set. An alternative way to look at it that works for arbitrary odd numbers p is to lift the p-power roots of unity in the complex numbers by the map x -> e2 pi ix/p.

If p is even, you probably have to make more choices.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.