proposition 4.66 prop:alg-direct-product-group

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:2396 · p. 87

Rests on

depends_on definition 4.65 Direct product of groups ¶
- depends_on definition 4.1 Cartesian product ¶
  - depends_on definition 3.28 Set ¶
- 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 4.21 Group ¶ ↺
proves proof ch:02-algebraic-structures@proof-24 ¶

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type	direction	node	provenance	where
`depends_on`	→	Direct product of groups	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2398
`depends_on`	→	Group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2398
`proves`	←	ch:02-algebraic-structures@proof-24	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2401