A group can be understood in different contexts, but generally it refers to a collection of two or more individuals or things that are connected or considered as a unit.

In Social and Everyday Contexts

• A group is a collection of two or more individuals who interact with one another, share common goals, and recognize themselves as part of a collective. This involves social relationships and interaction, which create a sense of identity and purpose among members

• Groups can be informal, like a group of friends, or formal, like a work team or organization. The key features include interaction, shared goals, and social bonds that keep the group cohesive

• In simple terms, a group is a number of people or things gathered or classified together because they have something in common

In Mathematics

• A group is a set equipped with a binary operation that combines any two elements to form another element of the set, satisfying three main axioms:
  • Associativity: The operation is associative.
  • Identity element: There is an element in the set that acts as an identity for the operation.
  • Inverse element: Every element has an inverse element in the set.
• For example, the integers with addition form a group because adding any two integers results in an integer, zero acts as the identity element, and every integer has an additive inverse (its negative)

Summary

• Social/General sense: A group is two or more people or things connected by social relationships, common interests, or shared goals.
• Mathematical sense: A group is a structured set with an operation fulfilling associativity, identity, and invertibility properties.

This dual meaning reflects the broad use of the term "group" across disciplines.