From the Cherlin-Zilber Conjecture via sharply $2$-transitive groups to the Burnside problem

Katrin Tent

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arXiv · 2606.18207

From the Cherlin-Zilber Conjecture via sharply $2$-transitive groups to the Burnside problem

Katrin Tent

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Abstract

We review the current state of the Cherlin-Zilber Algebraicity Conjecture on simple groups of finite Morley rank, which states that every such group is the group of $K$-rational points of an algebraic group for some algebraically closed field $K$. We will explain the relevance of sharply 2-transitive groups as a potential source of counterexamples and how the Burnside problem necessarily comes into the picture.

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Katrin Tent. 2026-06-16. From the Cherlin-Zilber Conjecture via sharply $2$-transitive groups to the Burnside problem. https://arxiv.org/abs/2606.18207

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