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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 the second derivative
Jack and Jill ran a 200 meter race. Jill ran the race in 25 seconds and won by 5 meters; that is Jack had run only 195 meters when Jill crossed the finish line.
A computer processes jobs on a first-come first-serve basis in a time-sharing environment. The jobs have Poisson arrival rates with an average of six minutes between arrivals.
Find the probability of random co-incidence, if the probability to get a certain value in both studies was the same, I would expect to have (125/1389)*38=3.41973 data-points with a larger value than the largest value in my study
Test the hypothesis for single proportion.
State whether it is inconsistent or has infinitely many solutions. If the system has infinitely many solutions, write the solution set with y arbitrary.
Effectiveness of a disease management program
Make the shape of the square.
chance of sitting in front of a crying baby all during a flight from California to Chicago does the poll show that Americans prefer buttered popcorn?
The problem that I'm having is that there is a nonconstant factor of (x^2+y^2+z^2)^(-1/2) appearing on the RHS of this equation, making it non-trivial to solve.
Use the semi-direct product construction to construct a nonabelian group of order pq, where p, q are prime numbers with q = 1 mod p
Find all maximal normal subgroups of Z[p] × Z[q], where p and q are relatively prime. Would the elements from Z[p] have to be one that are relatively prime to q and vice versa?
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