definition 3.58 Equivalence relation

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Supports

• depends_on definition 3.59 Equivalence class ¶
  • depends_on definition 4.58 Conjugacy classes ¶
    • depends_on definition 4.59 Conjugate subgroups ¶
      • depends_on definition 4.60 Normal subgroup ¶
        • depends_on proposition 4.63 Well-definedness of the coset product ¶
        • depends_on proposition 4.70 Characterization of the direct product ¶
        • depends_on proposition 4.75 The two factors inside the semidirect product ¶
        • depends_on proposition 4.77 When a semidirect product is direct ¶
        • depends_on theorem 4.64 Quotient group ¶
        • depends_on theorem 4.76 Internal characterization of the semidirect product ¶
  • depends_on definition 4.62 Cosets ¶
    • depends_on proposition 4.63 Well-definedness of the coset product ¶ ↺
  • depends_on definition 3.61 Quotient space ¶
  • depends_on theorem 3.60 Equivalence classes partition the set ¶
    • depends_on lemma A.10 lem:app-comp-welldefined ¶
      • depends_on lemma A.11 Truth lemma ¶
        • depends_on theorem A.12 Model existence ¶
• depends_on lemma A.10 lem:app-comp-welldefined ¶ ↺
• depends_on proposition 4.40 prop:alg-congruence-equiv ¶
  • depends_on proposition 4.41 prop:alg-zn-group ¶
    • depends_on example 4.69 The Cayley table of $\Z_2\times\Z_4$ ¶
• depends_on proposition 4.57 prop:alg-conjugacy-equiv ¶
  • depends_on definition 4.58 Conjugacy classes ¶ ↺
• depends_on proposition 4.61 prop:alg-coset-equiv ¶
  • depends_on definition 4.62 Cosets ¶ ↺
• depends_on theorem 3.60 Equivalence classes partition the set ¶ ↺