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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 writeG(bar)=G/A. Show that G acts(on the left) by conjugation on A byg(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.
p10-1 q-111. find the point on the line segment connecting p and q that is 14 of the way from p to
Describe the various decisions for Esil University that would be affected by the forecast for undergraduate applications.
Where N is the set of all nilpotent elements. "a" is nilpotent if a^n=0 for some positive integer n. N itself is an ideal.
the garica family has a budget. each month they use their income in the following manner 30 for food 25 for husehold
Find an equation in the form y=ms +b (where possible) for each line.
Solve the following linear system using Gaussian elimination.
Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counter example.
Linear and constant functions. Graph each function and state its domain and range. Absolute value functions. Graph each absolute value function and state its domain and range.
a trendy garment receives orders from three boutiques. the first boutique orders 25 jackets 75 shirts 75 pairs of
(If the expression is an exponential form, write it in radical form. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers)-m √(?2y?^5 )
Find the intervals of increase and decrease for f(x) = 6x3 + 54x2 - 228x - 7. Whaqt is an equation for the tangent line to the curve y = (3x2 + x - 1)9at the point where x = 0.
Discuss the general shape and location of each of your graphs - State the domain and range for each of your equations. Write them in interval notation and state whether each of the equations is a function or not giving your reasons for the answer.
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