Proof that If K is finite and F is an algebraic closure of K, then Aut K
Question:
Proof that If K is finite and F is an algebraic closure of K, then AutKF is abelian. Every element of AutKF (except 1F) has infinite order.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 75% (8 reviews)
First we will prove that AutKF is abelian Let and be two distinct automorphisms of F over K Since F ...View the full answer
Answered By
Isabel Seraspi
I have experience teaching math, science, and English to students of all ages. I have also worked as a tutor in a college setting, helping students with their homework and preparing them for exams.
I believe that tutoring is a great way to help students learn. It allows students to get one-on-one help with their studies, and it gives them the chance to ask questions and get immediate feedback. Tutoring can also be tailored to the individual needs of the student, which is why I believe it is so effective.
I have seen firsthand how tutoring can help students improve their grades and confidence. I have also seen how it can help students who are struggling with a particular subject. I believe that tutoring is a great way to help students learn and succeed in school.
0.00
0 Reviews
10+ Question Solved
Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
Question Posted:
Students also viewed these Mathematics questions
-
Let F be an algebraic closure of the field Q of rational numbers and let E F be a splitting field over Q of the set S = { x 2 + a | a Q} so that E is algebraic and Galois over Q (Theorem 3.11). (a)...
-
F is an algebraic closure of K if and only if F is algebraic over K and for every algebraic extension E of K there exists a K-monomorphism E F.
-
Proof that Let F be an algebraic extension of K such that every polynomial in K[x] has a root in F. Then F is an algebraic closure of K.
-
On January 1, 2010, Phelps Company purchased an 85% interest in Sloane Company for $955,000 when the retained earnings of Sloane Company were $150,000. The difference between implied and book value...
-
A prominent beta estimation service reports the beta of Comcast Corporation, a major cable TV operator, to be 1.45. The service claims to use weekly returns on the stock over the prior five years and...
-
How do construct validity and content validity differ? Why is each important to consider when establishing performance appraisal systems?
-
In a survey conducted for Money magazine by the ICR Survey Research Group, 26% of parents with collegebound high school children reported not having saved any money for college. The poll had a ". . ....
-
The condensed statements of Ipex Inc. follow: Required Rounding calculations to two decimal places: 1. Calculate each years current ratio. 2. Express the income statement data in common-size...
-
3. Given the bid-ask quotes for jpy/gbp 220-240, at what rate will: (a) Mr. Agbo purchase gbp? 2 MARKS (b) Mr. Agbo sell gbp? 2 MARKS (c) Mr. Debrah purchase jpy? 2 MARKS (d) Mr. Kwaku sell jpy? 2...
-
a. An analysis of WTI s insurance policies shows that $2,400 of coverage has expired. b. An inventory count shows that teaching supplies costing $2,800 are available at year-end. c. Annual...
-
If F is a finite dimensional Galois extension of K and E is an intermediate field, then there is a unique smallest field L such that E L F and L is Galois over K; furthermore where runs over Aut K...
-
Let E be an intermediate field. (a) If u F is separable over K, then u is separable over E. (b) If F is separable over K, then F is separable over E and E is separable over K.
-
Lithium is the source of tritium, which is the primary ?fuel? for a dt fusion reactor. (The deuterium, which his abundant and relatively cheap, can be considered as analogous to the air required for...
-
4. Consider the RC circuit shown below: R C C2 The capacitors are connected in parallel. Use C = 120 F, C = 30F, R = 5002, and = 40V. The capacitors are initially uncharged and at t=0 the switch is...
-
The DuPont equation shows the relationships among asset management, debt management, and profitability of improving the firm's performance. Its equation is: ratios. Management can use the DuPont...
-
38. A pendulum bob of mass 0.200 kg is pulled to one side such that it has a height of 0.50 m relative to its rest position (that is, its lowest point). It is then released so that it swings back and...
-
Let A in K ^ ( n \ times n ) be an ( n \ times n ) - matrix. Show that there ist a basis B of K ^ n that consists of eigenvectors of A .
-
Using the "you" view is an effective way for writers to avoid taking on blame in business messages. O True False
-
1. Which of the following is a question that companies should answer when preparing the business case for an IT investment? a. How much will it cost? b. What are the risks? c. What are the...
-
One Way Cellular accountants have assembled the following data for the year ended September 30, 2014: Prepare the operating activities section using the indirect method for One Way Cellulars...
-
What proportion of people in each group developed abnormal triglyceride levels over the course of the study? Are these proportions measures of prevalence, incidence, or neither? Ophthalmology One...
-
What test can be performed to compare the percentage of participants who developed abnormal triglyceride levels between the vitamin A group and the trace group? Ophthalmology One interesting aspect...
-
Implement the test in Problem 10.72, and report a two-tailed p-value? Ophthalmology One interesting aspect of the study described in Problem 10.68 is to assess changes in other parameters as a result...
-
How do warehouses and distribution centers differ? What is cross-docking and why might a company choose to cross-dock a product? What kinds of products can be delivered electronically? What kinds...
-
Strawberry Inc. has historically been an all-equity firm. The analyst expects EBIT to be $1.5B in perpetuity starting one year from now. The cost of equity for the company is 11.5% and the tax rate...
-
Guzman company received a 60- day, 5 % note for 54,000 dated July 12 from a customer on account. Determine the due date on note. Determine the maturity value of the note and journalize the entry of...
Study smarter with the SolutionInn App