Group definition is - two or more figures forming a complete unit in a composition. An assemblage of persons or objects gathered or located together; an aggregation: a group of dinner guests; a group of buildings near the road.

A group is a set \(S\) with an operation \(\circ: S\times S\rightarrow S\) satisfying the following properties: Identity: There exists an element \(e\in S\) such that for any \(f\in S\) we have \(e\circ f = f\circ e = f\). group synonyms, group pronunciation, group translation, English dictionary definition of group. Learn what is group. A group is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property.The operation with respect to which a group is defined is often called the "group operation," and a set is said to be a group "under" this operation. Define group. In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. Also find the definition and meaning for various math words from this math dictionary. n. 1. How to use group in a sentence. Inverses: For any element \(f\in S\) there exists \(g\in S\) such that \(f\circ =e\). 2. Group. Definition 2.1.0: Group.