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From Wikipedia, the free encyclopedia

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, 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

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