Math 361, Spring 2014, Assignment 8

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

1. Meet (of two subgroups of a group $G$).
2. Join (of two subgroups).
3. Product (of two subgroups).
4. Subnormal series.
5. Factors (of a subnormal series).
6. Isomorphic (subnormal series).
7. Refinement (of a subnormal series).
8. Saturated (subnormal series).
9. Composition series.
10. Composition factors.

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

1. Lemma relating joins to products.
2. First isomorphism theorem.
3. Second isomorphism theorem.
4. Third isomorphism theorem.
5. Jordan-Hölder Theorem.

Solve the following problems:

1. Section 34, problems 3 and 5.
2. Section 35, problems 1, 3, and 7.

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