Math 360, Fall 2017, Assignment 6

Mathematicians are like Frenchmen: whatever you say to them they translate into their own language, and forthwith it is something entirely different.

- Goethe

Read:

1. Section 6.

Carefully define the following terms, then give one example and one non-example of each:

1. Cyclic group.
2. Quotient (of an integer by a non-zero integer).
3. Remainder (of an integer modulo a non-zero integer).

Carefully state the following theorems (you do not need to prove them):

1. Classification of cyclic groups.
2. Theorem concerning subgroups of cyclic groups.
3. Theorem concerning integer division.

Solve the following problems:

1. Section 6, problems 1, 3, 5, 17, 18, 19, 22, 25, 26, 27, 33, 34, 35, 36, and 37.

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