Math 361, Spring 2013, Assignment 10

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

1. Letter (in a given alphabet \(S\)).
2. Syllable.
3. Word.
4. Elementary contraction.
5. Elementary expansion.
6. Equivalence of words.
7. Reduced word.
8. Free group (on a set \(S\)).
9. Rank (of a free group).
10. Group presentation.
11. Generators of a presentation.
12. Relators of a presentation.
13. Consequences of a set of relators.
14. Relations of a presentation.
15. Finite presentation.
16. Finitely presented group.
17. Isomorphic presentations.

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

1. Theorem on homomorphisms from free groups (Theorem 39.12 in the text).
2. Theorem on homomorphic images of free groups (Theorem 39.13 in the text).

Do the following problems:

1. Section 39, problems 1, 3, and 4.
2. Section 40, problems 1, 2, 3, 4, and 5.