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)
Lattice

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

Topological / 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

Elliptic curve

Linear algebraic group

Abelian variety

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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