Relation GROUP

• Defined in theory: Abstract-algebra
• Source code: abstract-algebra.lisp

Slots on this relation:

Instance-Of: Relation

Arity: 3

Equivalence Axioms:

(<=> (Group ?Domain ?Op ?Id)
     (And (Binary-Operator-On ?Op ?Domain)
          (Associative ?Op ?Domain)
          (Identity-Element-For ?Id ?Op ?Domain)
          (Invertible ?Op ?Id ?Domain)))

Other Related Axioms:

(<=> (Group ?Domain ?Op ?Id)
     (And (Binary-Operator-On ?Op ?Domain)
          (Associative ?Op ?Domain)
          (Identity-Element-For ?Id ?Op ?Domain)
          (Invertible ?Op ?Id ?Domain)))

(Subrelation-Of Abelian-Group Group)

(<=> (Abelian-Group ?Domain ?Op ?Id)
     (And (Group ?Domain ?Op ?Id) (Commutative ?Op ?Domain)))

(<=> (Division-Ring ?Domain ?Plus-Op ?Zero-Id ?Mult-Op ?One-Id)
     (And (Ring ?Domain ?Plus-Op ?Zero-Id ?Mult-Op ?One-Id)
          (Group (Kappa (?X)
                        (And (Instance-Of ?X ?Domain)
                             (/= ?X ?Zero-Id)))
                 ?Mult-Op
                 ?One-Id)))