Groups of Finite Morley Rank and Even Type with Strongly Closed Abelian Subgroups

Altınel, Tuna; Borovik, Alexandre; Cherlin, Gregory

doi:10.1006/jabr.2000.8345

Cited by 11 publications

(12 citation statements)

References 20 publications

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“…The following result was proved in [3] though stated somewhat differently; our formulation comes from [4]. …”

Section: O G Is the Largest Connected Definable Normalmentioning

confidence: 83%

“…The following two facts were proved in [4] under a restrictive hypothesis ("tameness") which can now be eliminated using Jaligot's classification (Fact 2.11). This is clear from the presentation in [4], where the theorems were given explicitly in the form of the existence of a weakly embedded subgroup in a minimal counterexample, in the absence of a tameness hypothesis.…”

Section: Abelian Sylow Subgroups and Standard Componentsmentioning

confidence: 93%

“…All we need from previous papers in the series are the main results of [4,21], reviewed in the next section. Modulo standard group theoretic facts and some general properties of groups of finite Morley rank the present paper is self-contained.…”

Section: Theorem 35 C G T Let G Be a Simple K * -Group Of Finite Mmentioning

confidence: 98%

“…In particular the definable connected 2 ⊥ -sections of G are solvable. Fact 2.21 [4]. Let H be a connected K-group of finite Morley rank of even type such that…”

Section: Fact 219 Let N Be a Definable Connected Nilpotent P-group mentioning

confidence: 98%

“…Fact 2.25 [4]. Let H be a connected K-group of finite Morley rank and even type, and let L be a definable quasisimple subgroup of …”

Section: Fact 219 Let N Be a Definable Connected Nilpotent P-group mentioning

confidence: 99%

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Pushing Up and C(G,T) in Groups of Finite Morley Rank of Even Type

2002

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“…The following result was proved in [3] though stated somewhat differently; our formulation comes from [4]. …”

Section: O G Is the Largest Connected Definable Normalmentioning

confidence: 83%

Section: Abelian Sylow Subgroups and Standard Componentsmentioning

confidence: 93%

Section: Theorem 35 C G T Let G Be a Simple K * -Group Of Finite Mmentioning

confidence: 98%

“…In particular the definable connected 2 ⊥ -sections of G are solvable. Fact 2.21 [4]. Let H be a connected K-group of finite Morley rank of even type such that…”

Section: Fact 219 Let N Be a Definable Connected Nilpotent P-group mentioning

confidence: 98%

“…Fact 2.25 [4]. Let H be a connected K-group of finite Morley rank and even type, and let L be a definable quasisimple subgroup of …”

Section: Fact 219 Let N Be a Definable Connected Nilpotent P-group mentioning

confidence: 99%

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