Margulis–Platonov conjecture over number fields
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The question is whether for an absolutely almost simple simply connected group G over a number field k, every noncentral abstract normal subgroup of G(k) is the inverse image of an open normal subgroup of the product of G(kᵥ) over anisotropic nonarchimedean places.
Why it matters and what counts as progress
Why it matters: It seeks the full number-field normal-subgroup classification in the simply connected absolutely almost simple setting.
What counts as progress: Establish the full normal-subgroup classification for all simply connected absolutely almost simple groups over number fields.
How the problem developed
- 1979 · Conjecture [1]
Grigory Margulis Formulated the local subgroup description that became the Margulis–Platonov conjecture.
- 23 Sept 2026 · Classification [1]
OpenAI Reported the iff classification of abstract noncentral normal subgroups for absolutely almost simple, simply connected groups over number fields.
AI contribution
The Margulis–Platonov conjecture over number fields
For an absolutely almost simple simply connected group G over a number field k, every noncentral abstract normal subgroup of G(k) is the inverse image of an open normal subgroup of the product of G(kᵥ) over anisotropic nonarchimedean places.
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