The Margulis-Platonov conjecture on normal subgroups of groups of rational points

Lineage and corrections

VibeMathed record: The Margulis-Platonov conjecture on normal subgroups of groups of rational points evidence for this event

The Margulis-Platonov conjecture on normal subgroups of groups of rational points parent of this event

Companion: The Margulis-Platonov conjecture over global function fields evidence for this event

This event attributed to Unreleased internal OpenAI model

The Margulis-Platonov conjecture on normal subgroups of groups of rational points evidence for this event

Margulis, Finiteness of quotient groups of discrete subgroups (1979) evidence for this event

Theorem 1.1 (number fields): for $G$ absolutely almost simple and simply connected over a number field $k$, every noncentral normal subgroup $N\triangleleft G(k)$ equals $\delta_A^{-1}(W)$ for an open normal $W$ of $\prod_{v\in A}G(k_v)$; when $A$ is empty, $N=G(k)$. With Rapinchuk's theorem it gives the congruence subgroup property for $S$ of positive Dirichlet density in the split places. The October 5 companion proves the same over every global function field, including characteristic two. It does not settle Serre's congruence subgroup conjecture for finite $S$ or arbitrary infinite $S$. parent of this event