example 4.69 The Cayley table of $\Z_2\times\Z_4$

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:2467 · p. 88

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depends_on definition 4.37 Cayley table ¶
- 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 proposition 4.68 Direct product of abelian groups ¶
- depends_on definition 4.8 Commutativity; abelian structure ¶
  - depends_on definition 4.4 Internal binary operation; magma ¶ ↺
- 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 ¶ ↺
- proves proof ch:02-algebraic-structures@proof-25 ¶
depends_on proposition 4.41 prop:alg-zn-group ¶
- depends_on definition 4.8 Commutativity; abelian structure ¶ ↺
- depends_on definition 4.21 Group ¶ ↺
- depends_on proposition 4.40 prop:alg-congruence-equiv ¶
  - depends_on definition 4.21 Group ¶ ↺
  - depends_on definition 3.58 Equivalence relation ¶
  - proves proof ch:02-algebraic-structures@proof-10 ¶
- proves proof ch:02-algebraic-structures@proof-11 ¶

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type	direction	node	provenance	where
`depends_on`	→	Cayley table	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2488
`depends_on`	→	Direct product of abelian groups	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2488
`depends_on`	→	prop:alg-zn-group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2488