Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. let m/f and k/f be galois extensions with galois g

Let M/F and K/F be Galois extensions with Galois groups G = Gal(M/F) and H =...

70.2K

Verified Solution

Question

Advance Math

Let M/F and K/F be Galois extensions with Galois groups G =Gal(M/F) and H = Gal(K/F). Since M/F is Galois, and K/F is a fieldextension, we have the composite extension field K M.

Show that σ → (σ|M , σ|K) is ahomomorphism from Gal(K M/F) to G × H, and that it is one-to-one.[As in the notes, σ|X means the restriction of the map σto the subset X of its domain.]

Answer & Explanation Solved by verified expert
4.5 Ratings (639 Votes)
A composite of Galois extensions is Galois so K M F is Galois Any GalK M F restricted to M or K is an automorphism since M and K are both Galois over F So we get a    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Biology
1.2K views

(a) A full explanation of the role of the endocrine and nervous systems in maintaining homeostasis. (b)...

Biology
1.2K views

Bioinformatics: What could be some of the reasons why your query sequence did not exactly match the...

Physics
1.2K views

What changes in the atomic structure cause the absorption and emission of photons (light)? i) Absorption ii) Emission

Psychology
1.2K views

Sry guy I cant find subject to put this, so I put under Psychology. The subject: culture...

Biology
1.2K views

Molecular Genetics 1 Draw a nucleotide and label the three parts Draw a segment of...

Basic Math
1.2K views

Consider the following implication:"If you drink coffee then you won't be able to sleep."Which of...

Calculus
1.2K views

For the following parametric equation x t 1 y 3 2t t Give the value...

Accounting
1.2K views

Question 12 You deposit $500 today in a savings account that pays 6% interest, compounded...

Accounting
1.2K views

Define quantitative analysis. What are some of the organizations that support the use of scientific...

Accounting
1.2K views

Samson Company had the following balances and transactions during 2015 January 1 Beginning inventory; 20...

Accounting
1.2K views

*Problem 14-3 Oriole Inc. developed a new sales gimmick to help sell its inventory of...

Accounting
1.2K views

Chapter 7 HW 3 Required information P7-3 (Static) Evaluating Four Alternative Inventory Methods Based on...