Uniqueness cases in odd-type groups of finite Morley rank

dc.contributor.authorNesin, Ali
dc.date.accessioned2021-06-17T08:19:47Z
dc.date.available2021-06-17T08:19:47Z
dc.date.issued2008-02
dc.description.abstractThere is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. One of the major theorems in the area is Borovik's trichotomy theorem. The 'trichotomy' here is a case division of the generic minimal counterexamples within odd type, that is, groups with a large and divisible Sylow° 2-subgroup. The so-called 'uniqueness case' in the trichotomy theorem is the existence of a proper 2-generated core. It is our aim to drive the presence of a proper 2-generated core to a contradiction, and hence bind the complexity of the Sylow° 2-subgroup of a minimal counterexample to the Cherlin-Zilber conjecture. This paper shows that the group in question is a minimal connected simple group and has a strongly embedded subgroup, a far stronger uniqueness case. As a corollary, a tame counterexample to the Cherlin-Zilber conjecture has Prüfer rank at most two. © 2008 London Mathematical Society.en_US
dc.fullTextLevelFull Texten_US
dc.identifier.doi10.1112/jlms/jdm106
dc.identifier.issn0024-6107
dc.identifier.scopus2-s2.0-44649135246en_US
dc.identifier.urihttps://hdl.handle.net/11411/3819
dc.identifier.urihttps://doi.org/10.1112/jlms/jdm106
dc.identifier.wosWOS:000253917900015en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.issue1en_US
dc.language.isoenen_US
dc.nationalInternationalen_US
dc.numberofauthors3en_US
dc.pages240 - 252en_US
dc.publisherJohn Wiley and Sons Ltden_US
dc.relation.ispartofJournal of the London Mathematical Societyen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.titleUniqueness cases in odd-type groups of finite Morley rank
dc.typeArticle
dc.volume77en_US

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