Do I write p-th or pth?

No, "pth" is not grammatically wrong. The much more commonly used word "nth" is punctuated the same way (although with nth, it's also common to leave off italicization of the first letter).

Aside from grammar, there are other considerations. If the document is going to be submitted for publication, you should learn what the house style is, and listen to any editorial feedback you receive.

I can think of a possible reason for using a hyphen, like "p-th": it might make the structure of the word more obvious. This could help your readers understand what you mean more quickly.

But technically, since the p is italicized and the "th" is not, there is enough information either way to indicate how the word should be divided. Also, "pth" is, as mentioned earlier, parallel to "nth," and also to the normal number words ending in the suffix "th."

You can see that "pth" is used in this math book: Matrices and Determinoids, by C. E. Cullis.

I'd therefore recommend using "pth" without a hyphen.