Math 360, Fall 2018, Assignment 8

Mathematical proofs, like diamonds, are hard as well as clear, and will be touched with nothing but strict reasoning.

- John Locke, Second Reply to the Bishop of Worcester

Read:

1. Section 6.

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

1. $\left\langle S\right\rangle$ (the subgroup of a given group $G$, generated by the given subset $S$).
2. Cyclic subgroup.
3. Cyclic group.
4. Quotient and remainder (when a given integer $a$ is divided by a given non-zero integer $b$).

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

1. Classification of cyclic groups.

Solve the following problems:

1. Section 6, problems 1, 3, 8, 9, 13, 14, 17, 19, 33, 34, 35, 36, and 37.

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