E be a hite field of order p". finite a. Show that the Frobenius automorphism op has order n. noltinitod I. b. Deduce from part (a) that G(E/Z,) is cyclic of order n with generator op. [Hint: Remember that |G(E/F)| = {E : F} = [E : F] for a finite separable splitting field extension E over F.]

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 7E
Topic Video
Question
Section 51 number 14
of F in E. [Hint: Use Exercise 9.]
14. Let E be a finite field of order p".
a. Show that the Frobenius automorphism op has order n.
neltinitod LS
eldrin b. Deduce from part (a) that G(E/Z,) is cyclic of order n with generator o p. [Hint: Remember that
|G(E/F)| = {E : F} = [E : F]
o dudT (omi lo agm
lum to for a finite separable splitting field extension E over F.]
Transcribed Image Text:of F in E. [Hint: Use Exercise 9.] 14. Let E be a finite field of order p". a. Show that the Frobenius automorphism op has order n. neltinitod LS eldrin b. Deduce from part (a) that G(E/Z,) is cyclic of order n with generator o p. [Hint: Remember that |G(E/F)| = {E : F} = [E : F] o dudT (omi lo agm lum to for a finite separable splitting field extension E over F.]
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