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Journal of Algebra
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Journal of Algebra
Article . 2004
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Journal of Algebra
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A signalizer functor theorem for groups of finite Morley rank

A signalizer functor theorem for groups of finite Morley rank.
Authors: Burdges, Jeffrey;

A signalizer functor theorem for groups of finite Morley rank

Abstract

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 minimal counterexamples within odd type, i.e. groups with a divisibble connected component of the Sylow 2-subgroup. We introduce a charateristic zero notion of unipotence which can be used to obtain a connected nilpotent signalizer functor from any sufficiently non-trivial solvable signalizer functor. This result plugs seamlessly into Borovik's work to eliminate the assumption of tameness from his trichotomy theorem for odd type groups. This work also provides us with a form of Borovik's theorem for degenerate type groups.

Country
United Kingdom
Keywords

03C60; 20G99, Algebra and Number Theory, 20G99, groups of finite Morley rank, infinite simple groups, groups of odd type, Mathematics - Logic, Group Theory (math.GR), Simple groups, Cherlin-Zilber conjecture, Linear algebraic groups over arbitrary fields, involutions, FOS: Mathematics, Applications of logic to group theory, Classification theory, stability, and related concepts in model theory, 03C60, unipotence, Logic (math.LO), signalizer functors, Mathematics - Group Theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
22
Average
Top 10%
Top 10%
Green
hybrid