§3 — $M_{23}$ is simple

Proved

MathieuM23.m23_isSimpleGroup

by Lucas · Oct 4, 2026 · Mathlib 0df444a (Lean v4.33.1)

group-theorymathieu-group

The group $M_{23}=\langle g_1,g_2\rangle$ is simple: it is nontrivial and its only normal subgroups are $\{1\}$ and $M_{23}$ .

Simplicity (with trivial center) is the standing hypothesis of the rigidity framework of §2.

Preamble

import Definitions.Def_MathieuM23_Group

Formal statement

namespace MathieuM23

theorem m23_isSimpleGroup : IsSimpleGroup M23 := by sorry

end MathieuM23

Source

X. Huang, B. Jackson, K.-H. Lee, B. Poonen, R. Pries, S. Zhang, *The Mathieu group M23 is a Galois group over Q*, arXiv:2608.08538v1 (2026), https://arxiv.org/abs/2608.08538, p. 4, §3, first sentence ("a finite simple group")

Read-back

What the Lean code literally says, in plain math · Aristotle (Harmonic) — same agent as the drafter; non-blind

Disclosure — NON-BLIND read-back. This read-back was written by the same agent that drafted the Lean statement (Aristotle, by Harmonic), with full knowledge of the source paper and of the intended meaning. It is not independent, blind testimony and must not be mistaken for an independent audit; a reviewer should compare it against the Lean code directly.

Statement. The group $M_{23}=\langle g_1,g_2\rangle$ (as a group in its own right, under composition) is a simple group. This means it has at least two elements, and every normal subgroup $N$ of $M_{23}$ is either the trivial subgroup or all of $M_{23}$ . No hypotheses.

Human review

Endorsed by Shuze Chen · Oct 5, 2026
Confirmed by the moderator at approval.
Endorsed by Lucas · Oct 5, 2026
Confirmed by the mission captain (proposal self-audit).

View graph

§3 — M23M_{23}M23​ is simple

§3 — $M_{23}$ is simple