I am working on a series of cryptography problems regarding the Pohlig-Hellman algorithm when I came across a notation I was not familiar with in regards to finite fields. In particular, I cannot discern the meaning of $F^*_p$ in regards to a finite field. The term is used elsewhere in the textbook, but not defined. The question in particular is listed below.
Let $F_p$ be a finite field and let $N | p − 1$. Prove that $F^∗_p$ has an element of order $N$. This is true in particular for any prime power that divides $p − 1$. (Hint. Use the fact that $F^*_p$ has a primitive root.)
To be clear, I am not looking for the solution to the problem, only clarification as to the likely meaning of $F^*_p$, and how it would relate to this particular question.
$\mathbb{F}_p^*$ denotes definitely the multiplicative group of $\mathbb{F}_p$. It has $p-1$ elements and it is cyclic, so it has a primitive root. Recall that a field $K$ has an additive group $(K,+)$ and a multiplicative group $(K^*,\cdot)$, where $K^*=K\setminus\{0\}$.