User submissions are the sole responsibility of contributors, with TuteeHUB disclaiming liability for accuracy, copyrights, or consequences of use; content is for informational purposes only and not professional advice.

Answers (2)

Post Answer

manpreet Best Answer 3 years ago

Define the trace by

T r : F p n ⟶ F p n : x ⟼ x + x p + \dots + x p n - 1

Now define yet another mapping:

L : F p n ⟶ F p n : x ⟼ x p - x

I know that this is a linear mapping. My syllabus stated the following I could't prove:

The kernel of the map is $F_{p}$ .
If the equation $y^{p} - y = x$

0 views

0 shares

manpreet 3 years ago

The first claim follows from the fact that the Galois group of $F_{p^{n}} / F_{p}$ is generated by the Frobenius map $x \mapsto x^{p}$ . Thus, from Galois theory, the subfield of $F_{p^{n}}$ fixed by $G (F_{p^{n}} / F_{p})$ is exactly $F_{p}$ . For your second statement, recall that $Tr (y^{p}) = Tr (y)$ , now apply $Tr$ on both sides of the equation.

0 views 0 shares

No matter what stage you're at in your education or career, TuteeHUB will help you reach the next level that you're aiming for. Simply,Choose a subject/topic and get started in self-paced practice sessions to improve your knowledge and scores.

Popular Categories

The equation yp−y=x in finite fields.

Manpreet Singh

Answers (2)

manpreet Best Answer 3 years ago

manpreet 3 years ago

Similar Forum

Neet 2019 syllabus will change?

Syllabus in LaTeX

Does Hogwarts follow any specific syllabus for DADA?

Explore Other Libraries

Online Exams

Question Bank

Career News

Feeds

Full Forms

Dictionary

Interview Question

Gigs

Quotes

Lyrics

Videos

Courses

Blogs

Tutorials

Forum

Educators

Corporates

Tools

Related Searches

Important Course Queries Links

Join Our Community Today