What is the kernel of phi

Reference no: EM13179072

Prove that if the function, phi, G to G' (G and G' are groups) is a homonorphism then the kernel of phi is a normal subgroup of g.

Now let phi be the function from R to GL(2,R) where phi(x) is:
Cos(x) -sin(x)
Sin(x) Cos(x)

Prove that this is a homonorphism, what is the kernel of phi? And what is phi(R)?

Reference no: EM13179072

Questions Cloud

Fears of radiation exposure from normal use of detectors : Fears of radiation exposure from normal use of such detectors are largely unfounded. Identify reasons why ^241Am smoke detectors are perfectly safe.

Find the intervals : find the intervals on which f(x) is increasing and decreasing and find the x- and y- coordinates of all the local extrema

Determine the whole number of standard deviations : Determine the whole number of standard deviations that includes all data values.

Discuss industry concentration-demand and market conditions : In the 1990s, five firms supplied amateur color film in the United States: Kodak, Fuji, Konica, Agfa, and 3M. From a technical viewpoint, there was little difference in the quality of color film produced by these firms, yet Kodak's market share wa..

What is the kernel of phi : Prove that this is a homonorphism, what is the kernel of phi? And what is phi(R)?

What is the likelihood that they will all work : a company owns 400 laptops.each laptop has an 8% probability of not working. you randomly select 20 laptops for your salespeople. a. what is the likelihood that 5 will be broken? b. what is the likelihood that they will all work? c. what is the li..

Find the dimensions of the can which minimize the amount : A soda can is to hold 12 fluid ounces. Suppose that the bottom and the top are twice as thick as the sides. Find the dimensions of the can which minimize the amount of material used.

Compute the predetermined overhead rate under current method : Compute the predetermined overhead rate under the current method, and determine the unit product cost of each product for the current year.

Calculate the demand for dollars and supply : Suppose the supply of dollars increase by 600 billion at each exchange rate. Explain if the increase in demand results from a large purchase b the Chinese of a new American-made airplane or a large purchase by Americans of new lower priced Chinese..

User Account

All Pages