Marion's finiteness conjecture for rigid triangle generation
Marion's finiteness conjecture for rigid triangle generation
Let be a simple algebraic group over an algebraically closed field of characteristic . For a positive integer , let be the dimension of the subvariety of elements of order dividing , and call a triple rigid for when
Call hyperbolic when . Marion's conjecture. Fix a prime . If is a rigid hyperbolic triple of primes for , then there are only finitely many positive integers such that the finite quasisimple group is -generated.
The conjecture concerns the finiteness of field extensions yielding triangle generation in the rigid case, extending the known results for rank-two groups. Its resolution status is not specified in the supplied text.
Progress summary
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Sources & referencesView supporting material
Primary source
Timothy C. Burness, “Simple groups, generation and probabilistic methods”, arXiv:1710.10434 (2017).
Additional references
3 papers in this index state this conjecture (2017). The statement above is taken from the most recent of them; the others are arXiv:1706.07641, arXiv:1706.01653.
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