Abstract Algebra: Theory and Applications

Express $(134)(354)$ 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.