Theorems

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On this page, you can add statements and proofs of Theorems, Lemmas and Corollaries. Add the theorem in the appropriate chapter and in the appropriate order. If a theorem is a named theorem, you should title your page with the theorem name, otherwise, title the page with the theorem number.

- Chapter 0 Theorems

- Chapter 2 Theorems
- Theorem 2.13 (Associativity of Composition)

- Chapter 3 Theorems
- Theorem 3.13 (Uniqueness of Identity Element)
- Theorem 3.14

- Chapter 4 Theorems

- Chapter 5 Theorems

- Chapter 6 Theorems
- Theorem 6.1 (every cyclic group is abelian)
- Theorem 6.6 (a subgroup of a cyclic group is cyclic)
- Corollary 6.7
- Theorem 6.10 (all infinite cyclic groups are isomorphic to $\mathbb{Z}$ under addition)
- Theorem 6.14
- Corollary 6.16

- Chapter 8 Theorems
- Chapter 9 Theorems
- Chapter 10 Theorems
- Theorem 10.1
- Theorem 10.10 (Theorem of Lagrange)
- Corollary10.11
- Lemma (Property of Cosets)
- Theorem 10.12
- Theorem 10.14

- Chapter 11 Theorems
- Chapter 13 Theorems
- Chapter 14 Theorems
- Chapter 15 Theorems
- Chapter 18 Theorems
- Chapter 19 Theorems
- Chapter 23 Theorems