List of group theory topics

Summary

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. 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.

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. Group theory is also central to public key cryptography.

Structures and operations edit

Basic properties of groups edit

Group homomorphisms edit

Basic types of groups edit

Simple groups and their classification edit

Permutation and symmetry groups edit

Concepts groups share with other mathematics edit

Mathematical objects making use of a group operation edit

Mathematical fields and topics making important use of group theory edit

Algebraic structures related to groups edit

Group representations edit

Computational group theory edit

Applications edit

Famous problems edit

Other topics edit

Group theorists edit

See also edit