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.

*Theorem Summaries

• Chapter 0 Theorems
  • Theorem 0.22

• 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
  • Theorem 4.15
  • Theorem 4.16
  • Theorem 4.17
  • Corollary 4.18

• Chapter 5 Theorems
  • Theorem 5.14
  • Theorem 5.17

• 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
  • Theorem 8.5
  • Lemma 8.15
  • Theorem 8.16
• Chapter 9 Theorems
  • Theorem 9.8
  • Theorem 9.15
  • Theorem 9.20
• 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
  • Theorem 11.2
  • Theorem 11.5
  • Corollary 11.6
  • Theorem 11.9
  • Theorem 11.12
  • Theorem 11.15
  • Theorem 11.16
  • Theorem 11.17
• Chapter 13 Theorems
  • Theorem 13.12 (Properties of Homomorphism)
  • Theorem 13.15
  • Corollary 13.18
  • Corollary 13.20
• Chapter 14 Theorems
  • Theorem 14.1
  • Theorem 14.4
  • Corollary 14.5
  • Theorem 14.9
  • Theorem 14.11
  • Theorem 14.13
• Chapter 15 Theorems
  • Theorem 15.8
  • Theorem 15.9
  • Theorem 15.15
  • Theorem 15.16
  • Theorem 15.18
  • Theorem 15.20
• Chapter 18 Theorems
  • Theorem 18.8
• Chapter 19 Theorems
  • Theorem 19.3
  • Corollary 19.4
  • Theorem 19.5
  • Theorem 19.9
  • Theorem 19.11
  • Corollary 19.12
  • Theorem 19.15
• Chapter 23 Theorems
  • Corollary 23.3