Group Actions and Transitive Permutations
Not what you're looking for?
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.
Purchase this Solution
Solution Summary
Group Actions and Transitive Permutations are investigated.
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Probability Quiz
Some questions on probability