Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
22. How many irreducible factors over over Q does x^48 - 1 have?

22. How many irreducible factors over over Q does x^48 - 1 have?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
ANSWER 22 only
21. Let K be the splitting field of x^23 - 1 over Q and zeta 3 be a 23rd primitive root of unity. Then what is order of the Galois group of K over Q? Enter your answer 22. How many irreducible factors over over Q does x^48 - 1 have? Enter your answer 23. The splitting field of f=(x^2-2)(x^2+1) over Q is Q(sqrt(2),i) because its roots are sqrt(2),- sqrt(2),i,-i. The Galois group of f contains the following automorphisms: sigma o: sqrt(2) → - sqrt(2) and tau T: i-i. Which subfield of the splitting field is fixed by sigma?
Transcribed Image Text:21. Let K be the splitting field of x^23 - 1 over Q and zeta 3 be a 23rd primitive root of unity. Then what is order of the Galois group of K over Q? Enter your answer 22. How many irreducible factors over over Q does x^48 - 1 have? Enter your answer 23. The splitting field of f=(x^2-2)(x^2+1) over Q is Q(sqrt(2),i) because its roots are sqrt(2),- sqrt(2),i,-i. The Galois group of f contains the following automorphisms: sigma o: sqrt(2) → - sqrt(2) and tau T: i-i. Which subfield of the splitting field is fixed by sigma?
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS