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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.
Find an example, of the BMI between man/woman and estimate a best fit line graphically. Develop an approximate linear model using the point slope form, the slope-intercept form or the standard form line.
Prove that the mapping a(g) = g^-1 for all g in G is an automorphism if and only if G is Abelian. An isomorphism from a group G onto itself is called an automorphism of G.
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There are three methods to solving Linear Systems with two Equations. They are the Graph method, the Elimination method, and the Substitution method.
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Problems on probability
Determine the height of the tree from the given information - Amman measures the angle between his base line and the line of sight to the base of the tree to be 510. How tall is tree, correct to the nearest M?
Estimation : Binomial Distribution Suppose T is a random variable such that
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What is the maximum that Ernesto should be willing to pay to play this game if he wants to be sure that on average, if he plays very many times, he shouldn't lose money?
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