Assertion: group | /r/HasProperty | set
Facets:
value: together
type: MANNER
value: with an operation ⋅
type: OTHER
value: in mathematics
type: OTHER
Source sentences:
text: In mathematics, a group is a set equipped with a binary operation that combines any two elements to form a third element in such a way that four conditions called group axioms are satisfied, namely closure, associativity, identity and invertibility.
text: A group is a set, G, together with an operation ⋅ (called the group law of G) that combines any two elements a and b to form another element, denoted a ⋅ b or ab.
text: For example, every group (as defined above) is also a set, so a group is a group object in the category of sets.
text: Group (mathematics), a set together with a binary operation satisfying certain algebraic conditions