Conclude that Aut G acts on the set of conjugacy classes of G.
Not what you're looking for?
Let C(a) be the conjugacy class in G containing a. Show that for a group G, if a <- G and f: G --> G is an automorphism, then b <- C(a) if and only if f(b) <- C(f(a)). Conclude that Aut G acts on the set of conjugacy classes of G.
Purchase this Solution
Solution Summary
The expert concludes that Aut G acts on the set of conjugacy classes of G.
Solution Preview
I have used LaTeX to generate the attached PDF file. Please refer to the attachment for clear notations.
Proposition. Let G be a group, a <- G, and C(a) = {gag^-1 : g <- G} be the conjugacy class of a. If f : G --> G is an ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Probability Quiz
Some questions on probability
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts