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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 inifinite