Math 3321 Review Test # 2 Spring 2002

Dr. Cordero

- Give the following definitions:

· Transposition

· Even (odd) permutations

· Equivalence relation

· Partition of a set

· Complete set of equivalence class representatives

· Greatest common divisor of two integers

· Relatively prime integers

· Least common multiple of two integers

· Standard form of an integer (prime factorization)

· Subgroup generated by an element

· Cyclic subgroup

· Order of an element

- Describe the subgroup of .
- State and prove Theorem 7.2.
- Describe the subgroups and of a group of permutations .
- Show that and are subgroups of the group .
- State in your own words Theorem 9.1 (understand it!).
- Study the equivalence relation given in Theorem 9.2. (Also, study the proof of Theorem 9.2).
- State and prove Theorem 10.1.
- Study the
__Division Algorithm.__ - Describe the group .
- What is ?
- Describe the
__Euclidean Algorithm__. - Study Theorem 12.2 and its Corollary.
- State in your
own words the
.__Fundamental Theorem of Arithmetic__ - State and prove Theorem 14.1.
- State and prove Theorem 14.2.
- State Theorem 14.3.