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