Math 360, Fall 2015, Assignment 12

Algebra begins with the unknown and ends with the unknowable.

- Anonymous

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

1. Fundamental theorem of homomorphisms.
2. Corollary relating the image of a homomorphism to the domain and the kernel.
3. Corollary concerning epimorphisms.

Solve the following problems:

1. Section 15, problems 1, 3, 5, and 7. (If you are not familiar with the fundamental theorem of finitely generated abelian groups, simply find a familiar group to which the given quotient group is isomorphic.)

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