Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
Contents
Description
The concept of a group is central to abstract algebra.
Various well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms.
Influence
Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra.
Branches
Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
Physical systems and applications
Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups.
Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science.
Public key cryptography
Group theory is central to public key cryptography.
Finite simple groups
One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of finite simple groups.
See also
External links
- Group theory @ Wikipedia
