proposition 4.53 The subgroups of $S_3$

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:1854 · p. 80

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 ¶
depends_on definition 4.36 Subgroup ¶
- depends_on definition 4.21 Group ¶ ↺
proves proof ch:02-algebraic-structures@proof-17 ¶

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type	direction	node	provenance	where
`depends_on`	→	Permutation group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1861
`depends_on`	→	Subgroup	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1861
`proves`	←	ch:02-algebraic-structures@proof-17	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1864