Assertion: abelian group's element | /r/HasAspect | inverse
Facets:
value: in #g#
type: LOCATION
Source sentences:
text: , every element has an inverse, the operation is associative).
text: Every bijection has an inverse function that undoes its action, and thus each element of a symmetric group does have an inverse which is a permutation too.
text: =e•a=a# Each element of #G# has an inverse in #G#
text: For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid.
text: A group that satisfies the commutative law Classified under: Nouns denoting cognitive processes and contents Synonyms: Abelian group; commutative group Hypernyms ("Abelian group" is a kind of...): group; mathematical group (a set that is closed, associative, has an identity element and every element has an inverse)
text: These require that the group be closed under the operation (the combination of any two elements produces another element of the group), that it obey the associative law, that it contain an identity element (which, combined with any other element, leaves the latter unchanged), and that each element have an inverse (which combines with an element to produce the identity element).
text: e; so every element has an inverse.