definition 4.49 Permutation group

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:1660 · p. 78

Rests on

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 4.2 Binary operation ¶
- 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 4.3 Algebraic structure ¶ ↺
    - depends_on definition 4.4 Internal binary operation; magma ¶
      - depends_on definition 4.3 Algebraic structure ¶ ↺
      - depends_on definition 4.2 Binary operation ¶ ↺
depends_on definition 4.48 Symmetric group ¶
- depends_on definition 3.47 Bijective map ¶

depends_on proposition 4.50 Cardinal of the permutation group ¶
- depends_on proposition 4.52 $S_3$ is a smallest non-abelian group ¶
depends_on proposition 4.53 The subgroups of $S_3$ ¶
depends_on theorem 4.56 Cayley's theorem ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1667
`depends_on`	→	Symmetric group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1667
`depends_on`	←	Cardinal of the permutation group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1706
`depends_on`	←	The subgroups of $S_3$	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1861
`depends_on`	←	Cayley's theorem	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1948