5.3: Reading Questions
Express \((1\,3\,4)(3\,5\,4)\) as a cycle, or a product of disjoint cycles. (Interpret the composition of functions in the order used by Sage, which is the reverse of the order used in the book.)
What is a transposition?
What does it mean for a permutation to be even or odd?
Describe another group that is fundamentally the same as \(A_3\text{.}\)
Write the elements of the symmetry group of a pentagon using permutations in cycle notation. Do this exercise by hand, and without the assistance of Sage.