Uniqueness cases in odd-type groups of finite Morley rank
Yükleniyor...
Dosyalar
Tarih
2008-02
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
John Wiley and Sons Ltd
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
There 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.
Açıklama
Anahtar Kelimeler
Kaynak
Journal of the London Mathematical Society
WoS Q Değeri
Q1
