# Automorphism group of dyadic rationals

I googled for this information but couldn't find anything...

What is the automorphism group of the additive group of the dyadic rationals $\mathbb{Z}[\frac{1}{2}]$ ?

-
It is its own endomorphism ring, so its automorphism group is just its group of units (acting by multiplication). $\langle -1 \rangle \times \langle 2 \rangle \cong C_2 \times C_\infty$ –  Jack Schmidt Jul 2 '12 at 16:37
Thank you very much ! –  AlexPof Jul 2 '12 at 19:16
@JackSchmidt: Would you like to make that an answer? –  Ilmari Karonen Jul 2 '12 at 19:51