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Parabolic 2-local subgroups in groups of finite Morley rank of even type

✍ Scribed by Tuna Altınel; Alexandre Borovik; Gregory Cherlin; Luis-Jaime Corredor

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
205 KB
Volume
269
Category
Article
ISSN
0021-8693

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📜 SIMILAR VOLUMES

Groups of Finite Morley Rank and Even Ty
Groups of Finite Morley Rank and Even Type with Strongly Closed Abelian Subgroups
✍ Tuna Altınel; Alexandre Borovik; Gregory Cherlin 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 279 KB

Conjecture 1 (Even Type Conjecture). Let G be a simple group of finite Morley rank of even type, with no infinite definable simple section of degenerate type. Then G is algebraic.

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Groups of Finite Morley Rank with Strongly Embedded Subgroups
✍ Tuna Altinel 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 295 KB

In this paper we prove the following theorem: THEOREM 1.5. Let G be an infinite, simple, K \*-group of finite Morley rank with a strongly embedded subgroup M. Assume that the Sylow 2-subgroups of G ha¨e infinitely many commuting in¨olutions. Then M is sol¨able. Ž . If, in addition, G is tame, then

An identification theorem for groups of
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✍ Ayşe Berkman; Alexandre V. Borovik 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 84 KB

The paper contains a construction of a definable BN-pair in a simple group of finite Morley rank and even type with a sufficiently good system of 2-local parabolic subgroups. This provides 'the final identification theorem' for simple groups of finite Morley rank and even type.