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Cherlin–Zilber Algebraicity Conjecture for Odd Type

Establish that every infinite simple group of finite Morley rank of odd type is isomorphic to a simple algebraic group over an algebraically closed field of odd or zero characteristic.

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Background

Simple groups of finite Morley rank are broadly divided into degenerate, odd, and even types, depending on the behavior of involutions and 2-torsion. The even-type case has been classified as algebraic, while the odd-type case remains a major target for the algebraicity conjecture.

This formulation isolates the odd-type case to align with progress in the classification program and focus efforts where current techniques are promising.

References

Conjecture 2. Cherlin-Zilber Algebraicity Conjecture for Groups of

Odd Type. Infinite simple groups of finite Morley rank and odd type are simple algebraic groups over algebraically closed fields of odd or zero characteristic.

— Primitive permutation groups of finite Morley rank and affine type (2405.07307 - Berkman et al., 12 May 2024) in Section 1.5