group theory


group theory

noun

Definition of GROUP THEORY

:  a branch of mathematics concerned with finding all mathematical groups and determining their properties

First Known Use of GROUP THEORY

1898

group theory

noun    (Concise Encyclopedia)

In modern algebra, a system consisting of a set of elements and an operation for combining the elements, which together satisfy certain axioms. These require that the group be closed under the operation (the combination of any two elements produces another element of the group), that it obey the associative law, that it contain an identity element (which, combined with any other element, leaves the latter unchanged), and that each element have an inverse (which combines with an element to produce the identity element). If the group also satisfies the commutative law, it is called a commutative, or abelian, group. The set of integers under addition, where the identity element is 0 and the inverse is the negative of a positive number or vice versa, is an abelian group. See also field theory.

Browse

Next Word in the Dictionary: group therapy
Previous Word in the Dictionary: group test
All Words Near: group theory

Seen & Heard

What made you want to look up group theory? Please tell us where you read or heard it (including the quote, if possible).