Infinite group

In group theory, an area of mathematics, an infinite group is a group whose underlying set contains infinitely many elements. In other words, it is a group of infinite order. The structure of infinite groups is often a question of mathematical analysis of the asymptotics of how various invariants grow relative to a generating set, or how a group acts on a topological or measure space. In contrast, the structure of finite groups is determined largely by methods of abstract algebra.

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