Infinite group

Algebraic structure → Group theory
Group theory

Basic notions

Group homomorphisms

List of group theory topics

Classification of finite simple groups

Lagrange's theorem

Frobenius group

Schur multiplier

Symmetric group S_n

Integers (Z)
Free group

PSL(2,Z)
SL(2,Z)

Topological and Lie groups

General linear GL(n)

Special linear SL(n)

Orthogonal O(n)

Euclidean E(n)

Special orthogonal SO(n)

Unitary U(n)

Special unitary SU(n)

Symplectic Sp(n)

Infinite dimensional Lie group

O(∞)
SU(∞)
Sp(∞)

Algebraic groups

Linear algebraic group

Reductive group

Abelian variety

Elliptic curve

In group theory, an area of mathematics, an infinite group is a group, of which the underlying set contains an infinite number of elements.

Examples

(R, +)
Infinite Lie groups
Infinite General linear groups

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