AATA Reading Questions

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Reading Questions 5.3 Reading Questions

1.

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.)

2.

What is a transposition?

3.

What does it mean for a permutation to be even or odd?

4.

Describe another group that is fundamentally the same as $A_3\text{.}$

5.

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.

Abstract Algebra: Theory and Applications

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Reading Questions 5.3 Reading Questions

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