Residually finite group

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

This is a variation of finiteness|Find other variations of finiteness |

Definition

Symbol-free definition

A group is said to be finitely approximable or residually finite if, for any non-identity element of the group, there is a normal subgroup of finite index not containing that element.

Formalisms

In terms of the residually operator

This property is obtained by applying the residually operator to the property: finite group
View other properties obtained by applying the residually operator

The group property of being residually finite is obtained by applying the residually operator to the group property of being finite.