Math 361, Spring 2013, Assignment 10
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Carefully define the following terms, then give one example and one non-example of each:
- Letter (in a given alphabet \(S\).
- Syllable.
- Word.
- Elementary contraction.
- Elementary expansion.
- Equivalence of words.
- Reduced word.
- Free group (on a set \(S\)).
- Rank (of a free group).
- Group presentation.
- Generators of a presentation.
- Relators of a presentation.
- Consequences of a set of relators.
- Relations of a presentation.
- Finite presentation.
- Finitely presented group.
- Isomorphic presentations.
Carefully state the following theorems (you need not prove them):
- Theorem on homomorphisms from free groups (Theorem 39.12 in the text).
- Theorem on homomorphic images of free groups (Theorem 39.13 in the text).
Do the following problems:
- Section 39, problems 1, 3, and 4.
- Section 40, problems 1, 2, 3, 4, and 5.
