The Margulis–Platonov conjecture over global fields

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Proves the Margulis–Platonov conjecture over every global field, including function fields of characteristic two. For an absolutely almost simple simply connected algebraic group G over k, every noncentral abstract normal subgroup of \(G(k)\) is the inverse image of an open normal subgroup in the finite product of its anisotropic nonarchimedean local groups.

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The paper states

Theorem 1.1

In The Margulis–Platonov conjecture over global function fields, 5 October 2026

Possible match to OpenAI’s description, selected from the papers’ main statements because it shares the most wording. No review confirming the selection is recorded.

The other possible matches are Corollary 1.2 (Positive-density congruence subgroup property) in The Margulis–Platonov conjecture over number fields () and Theorem 1.1 in The Margulis–Platonov conjecture over number fields ().

Let k be a global function field and let G be an absolutely almost simple simply connected k-group. If N\triangleleft G(k) and N\not\subseteq Z(G(k)), then

N=\delta_A^{-1}(W)

for an open normal subgroup W\triangleleft H_A. This holds in every positive characteristic, including when G is anisotropic over k.

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Papers

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The Margulis–Platonov conjecture over global function fields

5 October 2026, current edition.

Read it here PDF

We prove the Margulis–Platonov conjecture over every global function field, including characteristic two. For an absolutely almost simple simply connected algebraic group, every noncentral abstract normal subgroup of its rational points is the inverse image of an open normal subgroup of the finite product of its anisotropic local groups.

The Margulis–Platonov conjecture over number fields

23 September 2026, current edition.

Read it here PDF

We prove the Margulis–Platonov conjecture over number fields. For an absolutely almost simple simply connected group, every noncentral abstract normal subgroup of its rational points is the inverse image of an open normal subgroup of the product of its anisotropic nonarchimedean local groups.

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The Margulis–Platonov conjecture over global function fields cites The Margulis–Platonov conjecture over number fields.

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