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.

• (Z, +), the group of integers with addition is infinite
• 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

Finite group

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