Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $q=p^n$ for some prime $p$. The splitting field of $P\in \mathbb{F}_q[X]$ over $\mathbb{F}_q$ is $\mathbb{F}_{q^m}$ for some integer $m$, and is a Galois extension of $\mathbb{F}_q$. How can I find out about $m$, or the Galois group from the irreducible factors of $P$?

share|improve this question
add comment

1 Answer 1

up vote 0 down vote accepted

The degree of $F_{q^m}$ over $F_q$ is $m$, and the Galois group is the cyclic group of $m$ elements. In terms of $P$, $m$ is the least common multiple of the degrees of the irreducible factors of $P$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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