1. It is given that is a subgroup of GL2(Q). (a) Show that G= {(6) wit...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. It is given that is a subgroup of GL2(Q). (a) Show that G= {(6) wit N = = {(6) with a in (+1} and b in in Q} Now let : GS3 be a homomorphism. (c) Show that N< ker(). Hint: () = (1/6)6. (d) Determine the number of possible . with b in b in Q} is a normal subgroup of G and that there is an isomorphism G/N~ (±1). Hint: use the first isomorphism theorem. (b) Is it true that N = [G,G]? Hint: compute the commutator of some simple elements of G. 1. It is given that is a subgroup of GL2(Q). (a) Show that G= {(6) wit N = = {(6) with a in (+1} and b in in Q} Now let : GS3 be a homomorphism. (c) Show that N< ker(). Hint: () = (1/6)6. (d) Determine the number of possible . with b in b in Q} is a normal subgroup of G and that there is an isomorphism G/N~ (±1). Hint: use the first isomorphism theorem. (b) Is it true that N = [G,G]? Hint: compute the commutator of some simple elements of G.
Expert Answer:
Answer rating: 100% (QA)
a To show that N is a normal subgroup of G we need to show that for any g in G and n in N the conjug... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
This simulation question is based upon a true set of facts. The information contained in the simulation question was obtained from publicly available sources. Would there be an Increase in...
-
We showed in Example 15.6 that A 4 has no subgroup of order 6. The preceding exercise shows that such a subgroup of A 4 would have to be isomorphic to either Z 6 or S 3 . Show again that this is...
-
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
-
The symmetrical three-phase load is A-connected, with Z-(4+ j3) 22 and the phase voltage 220 V, find IL, IP, UL and P of the three loads. 7.(10 score) The symmetrical three-phase load is Y-connected....
-
The observer in the accelerating elevator of Example 5.8 would claim that the weight of the fish is T, the scale reading. This is obviously wrong. Why does this observation differ from that of a...
-
How many ways are there that no two students will have the same birth date in a size of 60 classes?
-
Argue the case for and against the political independence of central banks.
-
On June 1, 2015, Weller Corp. issued $2,000,000, 9%, 5-year bonds at face value. The bonds were dated June 1, 2015 and pay interest semiannually on June 1 and December 1. Financial statements are...
-
Sales Mix and Break-Even Sales Data related to the expected sales of kayaks and canoes for River Sports Inc. for the current year, which is typical of recent years, are as follows: Products Unit...
-
7. 8. 9. An experiment is conducted using a fin as shown below. Temperature readings are collected along the length of the fin, which is made from copper with k-400W/m.K. Tb=50C x1 X L = 0.5m x2 h x3...
-
A Procedure that inputs old_Manager_ID and new_manager_id. This store procedure will update all the departments with the old manager ID to the new manager id which is supplied as input parameters. a...
-
Determine the closed loop transfer function for the system in figure. Determine the values of K and Kh so that the system is stable. (b) Design Ge(s) as a PI controller such the system has 20% OS...
-
A skier of mass 68 kg is pulled up a slope by a motor-driven cable. (a) How much work is required to pull him 55 m up a 30 slope (assumed frictionless) at a constant speed of 2.2 m/s? 13,328 x Your...
-
Case study Kate (aged 32) and Emily (aged 31) are sisters. Kate works full-time as a nurse and Emily works in IT as a contractor, specialising in project management. Kate has been working for 10...
-
10. From the following information prepare marginal costing statement and calculate BEP and PVR Fixed cost Ro 120000 Variable cost RO 200000 Sales RO 1000000 Direct wages RO 150000 Direct materials...
-
Title: Request for Proposal - Market Research on Cheese in Canada Background Contexts: It has been documented that the consumption of cheese is an important aspect of Canadian food culture. Recent...
-
Evans Equipment sells, installs, and maintains manufacturing equipment. The typical sales contract includes the purchase of the equipment, installation, and a five-year maintenance contract. Most...
-
Walker, Inc., is an all-equity firm. The cost of the company's equity is currently 11.4 percent and the risk-free.rate is 3.3 percent. The company is currently considering a project that will cost...
-
Construct three different augmented matrices for linear systems whose solution set is x1 = 3, x2 = -2, x3 = -1.
-
Let F be a fixed 3 ( 2 matrix, and let H be the set of all matrices A in M2(4 with property that FA = 0 (the zero matrix in M3(4). Determine if H is a subspace of M2(4?
-
A is a 7 x 7 matrix with three eigenvalues. One eigenspace is two-dimensional, and one of the other eigenspaces is three-dimensional. Is it possible that A is not diagonalizable? Justify your answer.
-
A situation where quantity demanded is greater than quantity supplied is called a(n) _________.
-
At a price greater than the equilibrium price, a(n) _________, or excess quantity supplied, would exist. Sellers would be willing to sell _________ than demanders would be willing to buy. Frustrated...
-
If the price of zucchini increases, causing the demand for yellow squash to rise, what do we call the relationship between zucchini and yellow squash?
Study smarter with the SolutionInn App