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a) Show that if n is odd then the set of all n-cycles consists of two conjugacy classes of equal size in An
b) Let G be a transitive permutation group on the finite set A with |A|>1. Show that there is some g in G such that g(a) is not equal to a for all a in A. (Such an element g is called a fixed point free automorphism)
c) Let G be a group, let A be an abelian normal subgroup of G, and write
G(bar)=G/A. Show that G acts(on the left) by conjugation on A by g(bar)a=gag^-1, where g is any representative of the coset g(bar). Give an explicit exxample to show that this action is not well defined if A is not abelian.
Ps. For part c G(bar) stands for notation of G with a bar(line) on the top....I don't know how to better type this notation on this screen.
Isomorphisms and automorphisms, This week lecture is taught about Isomorphism, automorphism and Inner automorphism, but I don't understand what they are.
Vectors : Identities and Dot Products, How could you use the properties of the dot product to prove the following identities
Using one proportion Z test to determine
Equation of the hyperbola if equations of Asymptotes are given - Determine angles between the Asymptotes of the Hyperbola.
Solve the system using elementary row operations on the equations of the augmented matrix. Follow the systematic elimination proceedure.
Formulate this problem as an LP solve using Solver in Excel, From the sensitivity analysis, which warehouse site should have had more paper allocated to it at the start of the week and by how much per tonne would the overall cost of transport have..
Poisson Kernel and Harmonic Function, Let P_r(t)=R((1+z)/(1-z)), z=re^it be the Poisson kernel for the unit disc |z|
Probability: Random Dart. A dartboard has 3 areas: the main board has a radius of 9 inches; there is a circle with a radius of 5 inches
Which of the following can be solved by using a system of equations? Laura and Mark went to the movies and spent $29 on movie tickets and snacks. Mark paid $10 more than Laura. How much did each spend?
Look at the graph above and comment on the sign of D or the discriminant. Form the quadratic equation based on the information provided and find its solution.
Permutation and combination to find number of ways
Find the values of f(x) at which each of the following functions is discontinuous. Why is the function discontinuous at that value?
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