Let E be a finite field of order p n . a. Show that the Frobenius automorphism
Question:
Let E be a finite field of order pn.
a. Show that the Frobenius automorphism σp has order n.
b. Deduce from part (a) that G(E/Zp) is cyclic of order n with generator σp.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 85% (7 reviews)
a We know that the nonzero elements of E form a cyclic group E of ...View the full answer
Answered By
Tobias sifuna
I am an individual who possesses a unique set of skills and qualities that make me well-suited for content and academic writing. I have a strong writing ability, allowing me to communicate ideas and arguments in a clear, concise, and effective manner. My writing is backed by extensive research skills, enabling me to gather information from credible sources to support my arguments. I also have critical thinking skills, which allow me to analyze information, draw informed conclusions, and present my arguments in a logical and convincing manner. Additionally, I have an eye for detail and the ability to carefully proofread my work, ensuring that it is free of errors and that all sources are properly cited. Time management skills are another key strength that allow me to meet deadlines and prioritize tasks effectively. Communication skills, including the ability to collaborate with others, including editors, peer reviewers, and subject matter experts, are also important qualities that I have. I am also adaptable, capable of writing on a variety of topics and adjusting my writing style and tone to meet the needs of different audiences and projects. Lastly, I am driven by a passion for writing, which continually drives me to improve my skills and produce high-quality work.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Let E be a set in Rm. For each u: E R which has second-order partial derivatives on E, Laplace's equation is defined by a) Show that if u is C2 on E, then Îu = (u) on E. b) Show that if E R3...
-
Let A be an arbitrary vector, and let e be a unit vector in some fixed direction. Show that A = e(A e) + e x (A x e) what is the geometrical significance of each of the two terms of the expansion?
-
Let E be a nonempty Jordan region in R2 and f: E [0, ) be integrable on E. Prove that the volume of Ω = {(x, y, z): (x, y) E, 0 Vol(2) f dA.
-
Suppose a state was trying to decide whether to fund primary and secondary education with a property tax or an income tax. What implications might this choice have for land use in the state?
-
Singleton Inc. uses the accrual basis of accounting and had the following transactions during the year. a. Merchandise was sold to customers on credit. b. Purchased equipment to be used in the...
-
Name and describe briefly the five kinds of causes of poor performance.
-
Assume that Xinshans China sold merchandise to three customers during June on credit, as shown in the following Accounts Receivable Control account. Required (a) Explain why the control account and...
-
Jim Nance has been offered an investment that will pay him $500 three years from today. a. If his opportunity cost is 7% compounded annually, what value should he place on this opportunity today? b....
-
Factors which might cause a reduction in management's assigned penalty are called: a. Last chances. b. Second chances. c. Mitigating circumstances. d. Discharge circumstances.
-
Give an example of two finite normal extensions K 1 and K 2 of the same field F such that K 1 and K 2 are not isomorphic fields but G(K 1 / F) G(K 2 /F).
-
Referring to Example 48.17, find the following fixed fields in E = Q(2, 3). a. E {1.3} b. E { 3} c. E {2. 3} Data from in Example 48.17 Consider the field Q(2, 3). Example 31.9 shows that [Q(2, 3) :...
-
Assume the facts in E13-5, except that Matthewson Company has chosen not to accrue paid sick leave until used, and has chosen to accrue vacation time at expected future rates of pay without...
-
6 A car starts from the point A. At times after leaving 4, the distance of the car from A is s m, where s = 30t0.4t, 0 < t < 25. The car reaches the point B when t=25. a Find the distance AB. b Show...
-
Five elite track athletes volunteer to participate in an experiment to compare two brands of running shoes. Each athlete runs the 100-meter race twice, once wearing Brand A and once wearing Brand B....
-
Explain when in business it "makes sense" to recommend Long-Term Debt vs Lease Financing when developing/expanding a product?
-
The gas laws are active in our everyday lives. Please describe a situation in your life in which one of the gas laws applies to the world around you. Make sure to state which gas law applies and then...
-
List 3 different ways you can identify an employee's personal behaviour, self awareness and personality traits.
-
Why should a pen not be used in field note keeping?
-
(a) As Section 17.3 discusses, high-frequency sound waves exhibit less diffraction than low-frequency sound waves do. However, even high-frequency sound waves exhibit much more diffraction under...
-
Reconsider the previous exercise. Conduct a theory-based analysis. Report the test statistic and p-value and summarize your conclusions. Also, compute 95% confidence intervals as a follow up,...
-
A study of drinking habits of college students at a particular college produced the two-way table of counts shown in the following table table . Analyze these data with appropriate descriptive and...
-
Students (grades 46) in the Lansing, Michigan, area were asked, What is the most important goal in school: getting good grades, being popular, or excelling in sports. The data are tabled below. (The...
-
4. Define mobile phase and stationary phase? What are the differences between them?
-
(a) Give an example of a random experiment, where the number of members in the sample space is 3. (b) Using Venn diagram show that (AUB) = AC B, where AC = complement of A. (c) Give a combinatorial...
-
5. a) In a marathon, the median finishing time was 3:35:04 (three hours, 35 minutes, and four seconds). You finished in 3:34:10. Provide the interpretation and meaning of the median time, and discuss...
Study smarter with the SolutionInn App