proposition 4.61 prop:alg-coset-equiv
open in the book ·
parts/02-mathematical-methods/02-algebraic-structures.tex:2106
· p. 83
Rests on
-
depends_on
definition 4.36
Subgroup
¶
-
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 4.9
Neutral element
¶
-
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 4.11
Inverse element
¶
-
depends_on
definition 4.21
Group
¶
- depends_on definition 3.58 Equivalence relation ¶
- proves proof ch:02-algebraic-structures@proof-21 ¶
Supports
-
depends_on
definition 4.62
Cosets
¶
- depends_on proposition 4.63 Well-definedness of the coset product ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Subgroup | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2108 |
depends_on |
→ | Equivalence relation | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2108 |
depends_on |
← | Cosets | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2161 |
proves |
← | ch:02-algebraic-structures@proof-21 | declared | parts/02-mathematical-methods/02-algebraic-structures.tex:2111 |