proposition 4.41 prop:alg-zn-group

open in the book · parts/02-mathematical-methods/02-algebraic-structures.tex:1356 · p. 74

Rests on

depends_on definition 4.8 Commutativity; abelian 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 4.1 Cartesian product ¶
      - depends_on definition 3.43 Map ¶
  - depends_on definition 4.2 Binary operation ¶ ↺
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 4.3 Algebraic structure ¶ ↺
    - depends_on definition 4.4 Internal binary operation; magma ¶ ↺
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 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Commutativity; abelian structure	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1359
`depends_on`	→	Group	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1359
`depends_on`	→	prop:alg-congruence-equiv	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1359
`depends_on`	←	The Cayley table of $\Z_2\times\Z_4$	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2488
`proves`	←	ch:02-algebraic-structures@proof-11	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:1362