proposition 4.50 Cardinal of the permutation group

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:1704 · p. 78

Rests on

depends_on definition 4.49 Permutation group ¶
- 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 4.48 Symmetric group ¶
  - depends_on definition 3.47 Bijective map ¶
proves proof ch:02-algebraic-structures@proof-15 ¶

Supports

depends_on proposition 4.52 $S_3$ is a smallest non-abelian group ¶

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`	→	Permutation group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1706
`depends_on`	←	$S_3$ is a smallest non-abelian group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1819
`proves`	←	ch:02-algebraic-structures@proof-15	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1709