Linear groups of finite Morley rank
Alexandre Borovik, Jeffrey Burdges

TL;DR
This paper proves that certain non-algebraic simple groups of finite Morley rank either have no involutions or resemble bad groups, supporting the Cherlin-Zilber conjecture in this context.
Contribution
It establishes the absence of involutions in non-algebraic simple groups of finite Morley rank with definable field representations, advancing the understanding of their structure.
Findings
Non-algebraic simple groups with definable representations have no involutions.
Such groups either resemble bad groups or are algebraic.
Supports the Cherlin-Zilber conjecture for these groups.
Abstract
We show that a non-algebraic simple group of finite Morley rank with a definable representation over a field has no involutions, and otherwise resembles a bad group. In particular, the modern form of the Cherlin-Zilber alebaricity conjecture hold for such groups.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Operator Algebra Research · Computability, Logic, AI Algorithms
