gruppo

Gruppo is an Italian noun meaning a number of individuals or things regarded as a single unit. It can refer to a collection of people, animals, objects, or abstract entities that share a common attribute. In everyday language it appears in phrases such as un gruppo di amici, un gruppo di lavoro, un gruppo musicale, and in contexts like gruppo sanguigno, the concept of a blood type. The word is cognate with the English group and the French groupe; the precise origin is not settled, but the sense of a gathering or cluster is old.

Gruppo is masculine; the plural is gruppi; adjectives and determiners agree with the noun (un gruppo, i gruppi; un grande gruppo, grandi gruppi).

In social and organizational contexts it can refer to teams, study groups, committees, or other units, as well as to categories used in biology, linguistics, and data organization.

In mathematics, un gruppo denotes an algebraic structure: a nonempty set G equipped with a binary operation that combines any two elements to a third, satisfying associativity; there exists an identity element e with e·a = a = a·e for all a in G; and every element has an inverse. Groups may be finite or infinite; examples include the integers under addition (Z, +), the nonzero real numbers under multiplication (R*, ×), and the symmetric group Sn of permutations under composition. Group theory studies their properties and symmetries.