theorem 4.64 Quotient group

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:2325 · p. 86

Rests on

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 definition 3.58 Equivalence relation ¶
    - 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 4.21 Group ¶ ↺
- depends_on definition 4.36 Subgroup ¶ ↺
depends_on equation 4.35 eq:alg-coset-neutral ¶
depends_on equation 4.38 eq:alg-coset-product ¶
proves proof ch:02-algebraic-structures@proof-23 ¶

Supports

Nothing declares a dependency on this node yet.

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Normal subgroup	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2328
`depends_on`	→	eq:alg-coset-neutral	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2328
`depends_on`	→	eq:alg-coset-product	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2328
`proves`	←	ch:02-algebraic-structures@proof-23	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2331