**Group**, in mathematics, set that has a multiplication that is associative [*a*(*bc*) = (*ab*)*c* for any *a, b, c*] and that has an identity element and inverses for all elements of the set. Systems obeying the group laws first appeared in 1770 in Joseph-Louis Lagrange’s studies of permutations of roots of equations; however, the word *group* was first attached to a system of permutations by Évariste Galois in 1831. It was Heinrich Weber, in 1882, who first gave a purely axiomatic description of a group independently of the nature of its elements. Today, groups are fundamental entities in abstract algebra and are of considerable importance in geometry, physics, and chemistry.

Citation Information

Article Title:
Group

Website Name:
Encyclopaedia Britannica

Publisher:
Encyclopaedia Britannica, Inc.

Date Published:
12 June 2006

Access Date:
October 24, 2021