proposition 4.63 Well-definedness of the coset product

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:2271 · p. 85

Rests on

depends_on definition 4.62 Cosets ¶
- depends_on definition 3.59 Equivalence class ¶
  - depends_on definition 3.58 Equivalence relation ¶
- depends_on proposition 4.61 prop:alg-coset-equiv ¶
  - depends_on definition 4.36 Subgroup ¶
    - depends_on definition 4.21 Group ¶
      - depends_on definition 4.11 Inverse element ¶
      - depends_on definition 4.20 Monoid ¶
  - depends_on definition 3.58 Equivalence relation ¶ ↺
  - proves proof ch:02-algebraic-structures@proof-21 ¶
depends_on definition 4.60 Normal subgroup ¶
- depends_on definition 4.59 Conjugate subgroups ¶
  - depends_on definition 4.58 Conjugacy classes ¶
    - depends_on definition 3.59 Equivalence class ¶ ↺
    - depends_on proposition 4.57 prop:alg-conjugacy-equiv ¶
      - depends_on definition 4.21 Group ¶ ↺
      - depends_on definition 3.58 Equivalence relation ¶ ↺
      - depends_on proposition 4.27 Inverse of a product ¶
      - proves proof ch:02-algebraic-structures@proof-20 ¶
  - depends_on definition 4.36 Subgroup ¶ ↺
- depends_on definition 4.36 Subgroup ¶ ↺
depends_on equation 4.35 eq:alg-coset-neutral ¶
proves proof ch:02-algebraic-structures@proof-22 ¶

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Edges

type	direction	node	provenance	where
`depends_on`	→	Cosets	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2277
`depends_on`	→	Normal subgroup	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2277
`depends_on`	→	eq:alg-coset-neutral	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2277
`proves`	←	ch:02-algebraic-structures@proof-22	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2280