Show that a finite field of p n elements has exactly one subfield of p m elements
Question:
Show that a finite field of pn elements has exactly one subfield of pm elements for each divisor m of n.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 83% (6 reviews)
Let F be a finite field of p n elements containing up to isomorphism the prime field Z p Let m be a ...View the full answer
Answered By
Mary Boke
As an online tutor with over seven years of experience and a PhD in Education, I have had the opportunity to work with a wide range of students from diverse backgrounds. My experience in education has allowed me to develop a deep understanding of how students learn and the various approaches that can be used to facilitate their learning. I believe in creating a positive and inclusive learning environment that encourages students to ask questions and engage with the material. I work closely with my students to understand their individual learning styles, strengths, and challenges to tailor my approach accordingly. I also place a strong emphasis on building strong relationships with my students, which fosters trust and creates a supportive learning environment. Overall, my goal as an online tutor is to help students achieve their academic goals and develop a lifelong love of learning. I believe that education is a transformative experience that has the power to change lives, and I am committed to helping my students realize their full potential.
5.00+
4+ Reviews
22+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
A ball of mass 7.00 kg is hung by two cables attached to the walls as shown in the following figure. Calculate the tension in the horizontal cable. 35 m 2 (a) 48.0 N (b) 83.5 N (c) 68.6 N (d) 93.5 N
-
Two identical bar magnets lie next to one another on a table. Sketch the magnetic field lines if the north poles are at opposite ends. N S S N
-
How many people must be survey in order to be 95% confident that the estimate percentage within 2.5 percentage points of the true population percentage? a.n- Assume that nothing is known about the...
-
a) The sustainable yield (Y) of a fishery is Y = E-0.5E where E denotes fishing effort. If the cost per unit of effort is 0.5 and the price of fish is 1, what is sustainable yield (i) under open...
-
Psychologists concerned about self-injurious behaviors (smoking, eating fatty diets, drug abuse, etc.) worry about the effects of maternal smoking on the incidence of low birthweight babies, who are...
-
Armstrong Surgical Center (the Surgical Center) wished to establish an ambulatory surgery center in Armstrong County, Pennsylvania. At the time, Armstrong County Memorial Hospital (the Hospital) was...
-
How is the sales volume in dollars necessary to reach a target profit calculated? a. target profit unit contribution margin b. target profit contribution margin ratio c. (fixed expenses + target...
-
The Midtown Market purchases apples from a local grower. The apples are purchased on Monday at $2.00 per pound, and the market sells them for $3.00 per pound. Any apples left over at the end of the...
-
15. 16. What is the final product (major) 'A' in the given reaction? CH3 OH CH CH3 HCI + 'A' (major product) CH3 CH3 Cl CH (B) CH3 CH2-CH3 (A) CH3 CH (C) shiks CH=CH2 (D) Which of the following...
-
Find the degree and a basis for the given field extension. Be prepared to justify your answers. Q(2 + 3) over Q(2 + 3)
-
Classify the given a C as algebraic or transcendental over the given field F. If is algebraic over F, find deg(, F). = , F = R
-
Healthy Life Co. is an HMO for businesses in the Fresno area. The following account balances appear on Healthy Life's balance sheet: Common stock (3,000,000 shares authorized; 2,200,000 shares...
-
3. Create a spreadsheet modeling trajectories of geometric Brownian motion starting at 100 with a growth rate of 5 percent, which is also a risk-free rate, and volatility of 30 percent. Make a...
-
Describe how ethics can play a role in how messages are communicated as well as how they are perceived. Locate a real-world example not found in this module's resources and provide a brief summary of...
-
What is empowerment? How would you define empowerment? Are there disadvantages to empowering employees? What are the benefits of empowering employees?
-
Why is Mixed-Methods Research appropriate for Sears retailing company? Why other methods would not be appropriate?
-
Determine the acceptability of the project using payback period. Year Project "Y" 10 (25,000) 1st year 1,500 2nd Year 2,500 3rd year 5,000 4th year 10,000 5th Year 12,000
-
Use the graphing facilities of Maple to approximate solutions to the following nonlinear systems. a. b. sin(4x1 x2) 2x2 x1 = 0, c. x1(1 x1) + 4x2 = 12, (x1 2)2 + (2x2 3)2 = 25. d. 5x21 x22 =...
-
Suppose that fraction used = / 1.0 + 0.1Mt. for some parameter 1. Write the discrete-time dynamical system and solve for the equilibrium. Sketch a graph of the equilibrium as a function of ....
-
A major movie studio has just completed its latest epic, a musical comedy about the life of Attila the Hun. Because the movie is different (no sex or violence), the studio is uncertain about how to...
-
The high price of gasoline is likely to lead to less travel. An economist specializing in energy uses wanted to learn more about driving habits, and, in particular, distances traveled by cars, buses,...
-
The number of hits (views) is recorded at a high-volume Web site in a day. Provide a reasonable description of the sample space. There can be more than one acceptable interpretation of each...
-
1) What are the main changes taking place in organizational use of information systems? Which of these do you think is having the greatest impact on businesses? 2)What is the connection between...
-
In May 2012, Honda Motor Scooter India Pvt Ltd (HMSI), the Indian subsidiary of Honda Motor Company Ltd. (HMCL), launched the Dream Yuga motorcycle in the Indian two wheeler market to attract mass...
-
Comprehensive Master Budget Accounting 2302 Jeffrey Vaughn, president of Frame-It Company, was just concluding a budget meeting with his senior staff. It was November of 20x0, and the group was...
Study smarter with the SolutionInn App