A signalizer functor theorem for groups of finite Morley rank.

DOI10.1016/j.jalgebra.2003.08.015zbMath1053.20029arXivmath/0308049OpenAlexW2076435973MaRDI QIDQ1429903

Jeffrey Burdges

Publication date: 27 May 2004

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0308049

zbMATH Keywords

groups of finite Morley rankinvolutionsCherlin-Zilber conjectureinfinite simple groupsunipotencesignalizer functorsgroups of odd type

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Applications of logic to group theory (20A15) Simple groups (20E32) Classification theory, stability, and related concepts in model theory (03C45)

Related Items (24)

Tame minimal simple groups of finite Morley rank ⋮ The Bender method in groups of finite Morley rank. ⋮ A GENERATION THEOREM FOR GROUPS OF FINITE MORLEY RANK ⋮ On Weyl groups in minimal simple groups of finite Morley rank. ⋮ Weyl groups of small groups of finite Morley rank. ⋮ Structure of Borel subgroups in simple groups of finite Morley rank. ⋮ Unipotence in positive characteristic for groups of finite Morley rank ⋮ Lie rank in groups of finite Morley rank with solvable local subgroups. ⋮ Groups of Finite Morley Rank with Solvable Local Subgroups ⋮ Minimal connected simple groups of finite Morley rank with strongly embedded subgroups. ⋮ Minimal connected simple algebraic groups of odd type. ⋮ A generic identification theorem for \(L^*\)-groups of finite Morley rank. ⋮ Linearity of groups definable in o-minimal structures ⋮ Non-algebraic minimal connected simple groups of odd type. ⋮ SEMISIMPLE TORSION IN GROUPS OF FINITE MORLEY RANK ⋮ Groups of finite Morley rank with a generically sharply multiply transitive action ⋮ Algebraic ℚ-groups as abstract groups ⋮ Actions of Groups of Finite Morley Rank on Small Abelian Groups ⋮ Pseudo-tori and subtame groups of finite Morley rank ⋮ Signalizers and balance in groups of finite Morley rank. ⋮ Around unipotence in groups of finite Morley rank ⋮ Carter subgroups in tame groups of finite Morley rank ⋮ Sylow theory for p = 0 in solvable groups of finite Morley rank ⋮ CONJUGACY OF CARTER SUBGROUPS IN GROUPS OF FINITE MORLEY RANK

Cites Work

• Parabolic 2-local subgroups in groups of finite Morley rank of even type.
• Tame minimal simple groups of finite Morley rank
• Fields of finite Morley rank
• A GENERIC IDENTIFICATION THEOREM FOR GROUPS OF FINITE MORLEY RANK
• A Hall Theorem for ω-Stable Groups
• Groups of mixed type
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