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On Groups of Finite Morley Rank with Weakly Embedded Subgroups

✍ Scribed by Tuna Altınel; Alexandre Borovik; Gregory Cherlin

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
329 KB
Volume
211
Category
Article
ISSN
0021-8693

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📜 SIMILAR VOLUMES

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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

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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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Let p be a prime number and K be an algebraically closed field of characteristic p. Let G be a finite group and B be a (p-) block of G. We denote by l B the number of isomorphism classes of irreducible KG-modules in B. Let D be a defect group of B and let B 0 be the Brauer correspondent of B, that i