definition 4.58 Conjugacy classes

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:2054 · p. 82

Rests on

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 4.11 Inverse element ¶
    - depends_on definition 4.9 Neutral element ¶
      - depends_on definition 4.3 Algebraic structure ¶
  - depends_on definition 4.20 Monoid ¶
    - depends_on definition 4.9 Neutral element ¶ ↺
    - depends_on definition 4.18 Semigroup ¶
      - depends_on definition 4.6 Associativity ¶
      - depends_on definition 4.4 Internal binary operation; magma ¶
- depends_on definition 3.58 Equivalence relation ¶ ↺
- depends_on proposition 4.27 Inverse of a product ¶
  - depends_on definition 4.21 Group ¶ ↺
  - depends_on proposition 4.23 Uniqueness of the inverse element ¶
    - depends_on definition 4.21 Group ¶ ↺
    - proves proof ch:02-algebraic-structures@proof-4 ¶
  - proves proof ch:02-algebraic-structures@proof-8 ¶
- proves proof ch:02-algebraic-structures@proof-20 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Equivalence class	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2062
`depends_on`	→	prop:alg-conjugacy-equiv	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2062
`depends_on`	←	Conjugate subgroups	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2077