Infinite group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions


An infinite group is a group whose order is infinite, i.e., the underlying set of the group has infinitely many elements. The order of the group may be any infinite cardinal (see there exist groups of every order).

Every group is either an infinite group or a finite group.

In general, group theory results are proved either for finite groups or for all groups. It is generally rare for a result to be proved specifically for infinite groups, but there do exist some results of that sort.