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About: Random group     Goto   Sponge   NotDistinct   Permalink

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

Type: yago:Abstraction100002137yago:Possession100032613yago:Property113244109yago:Relation100031921eventyago:WikicatPropertiesOfGroups New Facet based on Instances of this Class

In mathematics, random groups are certain groups obtained by a probabilistic construction. They were introduced by Misha Gromov to answer questions such as "What does a typical group look like?" It so happens that, once a precise definition is given, random groups satisfy some properties with very high probability, whereas other properties fail with very high probability. For instance, very probably random groups are hyperbolic groups. In this sense, one can say that "most groups are hyperbolic".