Math 360, Fall 2015, Assignment 11

The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

- Saint Augustine

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

1. Quotient group (your book calls these factor groups).
2. Canonical projection.

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

1. Theorem on the normality of kernels.
2. Theorem characterizing when coset multiplication is well-defined.

Solve the following problems:

1. Section 14, problems 1, 3, 5, 7, 9, 11, and 24.

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