As usual, as I am not quite diligent a user of this website, I cannot make sure whether or not this has already been posted, but I have tried.
In the last winter, I for the first time found the book Basic Number Theory by André Weil, which I found an amount of doubts therein; I thought this is casual for a student with barely any acquaintance with the locally compact groups then. After some time spent on this topic, even though I can solve a lot of problems right now, there are some of them refusing to get into my mind, one of which is this.
On the page 13 of the book, line 6 states that $\Gamma$ is generated by $q$, the number of elements of the residual field; however, line 16 states that it is generated by an element <1; moreover, I do not even know why it can be generated by only one element.
Here, $K$ is a locally compact field, $\Gamma$ the image of $K^{*}$ under $\bmod_{K}$, where $\bmod_{K}$ is the module function on the field, obtained from the unicity of the Haar measure. Also, q is the number of elements of $R/P$, the residual field.
Since only some hints are required here, I tag this post as a homework; if this is somehow inappropriate, please notice me.
Best thanks and regards here.