Uniform bounded generation conjecture for principal congruence subgroups
Uniform bounded generation conjecture for principal congruence subgroups
Let be a ring of algebraic integers with infinitely many units, let be a non-trivial ideal in , and let be an irreducible root system of rank at least . Write for the principal congruence subgroup and
Uniform bounded generation conjecture. There is a minimal constant proportional to and independent of and such that
This conjecture asks for a bound on bounded generation by a conjugacy-invariant collection that depends only on the root system, rather than on the ring or ideal. The supplied text gives no evidence that the conjecture has been resolved.
Progress summary
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Sources & referencesView supporting material
Primary source
Alexander Alois Trost, “Bounded generation for congruence subgroups of Sp_4(R)”, arXiv:2101.02301 (2021).
Additional references
2 papers in this index state this conjecture (2020–2021). The statement above is taken from the most recent of them; the others are arXiv:2012.12328.
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