n. 1. Define group. Also find the definition and meaning for various math words from this math dictionary. Learn what is group. An assemblage of persons or objects gathered or located together; an aggregation: a group of dinner guests; a group of buildings near the road. 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. How to use group in a sentence. 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. Group definition is - two or more figures forming a complete unit in a composition. 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. Definition 2.1.0: Group. 2. group synonyms, group pronunciation, group translation, English dictionary definition of group. Inverses: For any element \(f\in S\) there exists \(g\in S\) such that \(f\circ =e\).