Infinite group

In group theory, an area of mathematics, an infinite group is a group whose underlying set contains an infinite number of elements. In other words, it is a group of infinite order.

Examples

• (Z, +), the group of integers with addition is infinite, as is (Q, +) the group of rational numbers with addition
• Non-discrete Lie groups are infinite. For example, (R, +), the group of real numbers with addition is an infinite group
• The general linear group of order n > 0 over an infinite field is infinite
• The Infinite dihedral group
• The Tarski monster group
• The Prüfer p-group

See also

Finite group