Let H and K be subgroups of a group G. Define ~ on G by a ~
Question:
Let H and K be subgroups of a group G. Define ~ on G by a ~ b if and only if a = hbk for some h ∈ H and some k ∈ K.
a. Prove that ~ is an equivalence relation on G.
b. Describe the elements in the equivalence class containing a ∈ G. (These equivalence classes are called double cosets.)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 42% (7 reviews)
a Reflexive We have a eae where e H and e K so a a S...View the full answer
Answered By
Nazrin Ziad
I am a post graduate in Zoology with specialization in Entomology.I also have a Bachelor degree in Education.I posess more than 10 years of teaching as well as tutoring experience.I have done a project on histopathological analysis on alcohol treated liver of Albino Mice.
I can deal with every field under Biology from basic to advanced level.I can also guide you for your project works related to biological subjects other than tutoring.You can also seek my help for cracking competitive exams with biology as one of the subjects.
3.30+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Let H and K be subgroups of a group G, where e is the identity of G. Prove that if |H| = 10 and |K| = 21, then H K = {e}.
-
Let H and K be subgroups of a group G. Ask you to establish necessary and sufficient criteria for G to appear as the internal direct product of H and K. Let H and K be groups and let G = H x K....
-
Let H and K be subgroups of a group G satisfying the three properties listed in the preceding exercise. Show that for each g G, the expression g = hk for h H and k E K is unique. Then let each g be...
-
Refer to Example 9. After how many seconds will the rocket be (a) 240 ft above the ground? (b) 112 ft above the ground? Data from in Example 9 EXAMPLE 9 Using a Quadratic Function in an Application...
-
What does Rule 102 mean in stating that a CPA should not subordinate judgment?
-
Which statements about the following line of code are correct? (Choose three.) throw new IllegalArgumentException (); A. The method where this is called must declare a compatible exception. B. The...
-
5. Consider the same 3-year swap. Suppose you are a dealer who is paying the fixed oil price and receiving the floating price. Suppose that you enter into the swap and immediately thereafter all...
-
Based upon the data presented in Exercise 2-13, (a) Prepare an unadjusted trial balance, listing the accounts in their proper order. (b) Based upon the unadjusted trial balance, determine the net...
-
CAN YOU PLEASE HELP ME COMPLETE THE RRST OF THIS PROBLEM I TRIED THIS PROBLEM TWO WAYS AND BOTH VALUES DIDNT WORK Demarco and Janine Jackson have been married for 20 years and have four children (no...
-
What was Lakesides gross profit for January? a. $7,500 b. $ 0 c. $1,900 d. $5,600
-
In analogy with Examples 8.7 and 8.10, consider a regular plane n-gon for n 3. Each way that two copies of such an n-gon can be placed, with one covering the other, corresponds to a certain...
-
Let A be a set, B a subset of A, and let b be one particular element of B. Determine whether the given set is sure to be a subgroup of S A under the induced operation. Here [B] = {(x) |x B}. { S A...
-
Why is it important for reports to be: A. Succinct? B. Comparable in design? C. Distributed only to intended users? D. Timely?
-
A year-end cut-off error occurred in 2017. A large shipment of nonperishable supplies arrived from South America on the last day of 2017 and had been left in the shipping containers outside the main...
-
15. [5] It's not so difficult to incorporate time-varying volatility into the BSM model as long as the time variation is not random. Assume a BSM economy, but this time, assume that the volatility of...
-
3.6. Explain and discuss the potential benefits to be gained by using blade twist, plan- form taper, low solidity, large radius, and low rotational speed for the main rotor of a heavy lift helicopter...
-
2. A VRM (Voltage Regulator Modul) is used to supply the voltageto the CPU of a computer. In the new generation of microprocessors,whose power consumption is 100W, the input voltage to the VRM is12V...
-
Alvarado Company produced 6,400 units of product that required 5.5 standard direct labor hours per unit. The standard variable overhead cost per unit is $5.80 per direct labor hour. The actual...
-
Mastercard, Inc., completed a ten-for-one stock split on January 22, 2014. Immediately before the stock split there were 120.38 million shares outstanding at a price of $826.00 per share. After the...
-
Consider the reaction of acetic acid in water CH 3 CO 2 H(aq) + H 2 O(l) CH3CO 22 (aq) + H 3 O + (aq) where Ka 5 1.8 3 1025. a. Which two bases are competing for the proton? b. Which is the stronger...
-
If we assume (a) serum cholesterol is normally distributed, (b) the cholesterol levels within each sample consist of independent observations, and (c) the standard deviations for men and women are...
-
Suppose a larger study is planned. How many participants are needed to detect a difference of 1 unit in mean balance score with 80% power if the number of participants in each group is intended to be...
-
What is your best estimate of the proportion of RA and OA patients with impaired balance, where impaired balance is defined as a balance score ¤2 and normality is assumed? Rheumatology A study...
-
Break-Even Sales and Sales to Realize Income from Operations For the current year ending October 31, Yentling Company expects fixed costs of $537,600, a unit variable cost of $50, and a unit selling...
-
You buy a stock for $35 per share. One year later you receive a dividend of $3.50 per share and sell the stock for $30 per share. What is your total rate of return on this investment? What is your...
-
Filippucci Company used a budgeted indirect-cost rate for its manufacturing operations, the amount allocated ($200,000) is different from the actual amount incurred ($225,000). Ending balances in the...
Study smarter with the SolutionInn App