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About: Residual property (mathematics)     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatPropertiesOfGroups, within Data Space : dbpedia.org associated with source document(s)

Type: yago:Abstraction100002137yago:Possession100032613yago:Property113244109yago:Relation100031921yago:WikicatPropertiesOfGroups New Facet based on Instances of this Class

In the mathematical field of group theory, a group is residually X (where X is some property of groups) if it "can be recovered from groups with property X". Formally, a group G is residually X if for every non-trivial element g there is a homomorphism h from G to a group with property X such that . More categorically, a group is residually X if it embeds into its pro-X completion (see profinite group, pro-p group), that is, the inverse limit of the inverse system consisting of all morphisms from G to some group H with property X.