Breakthrough Tracker record

A characteristic-two counterexample to Wehlau’s Noether-number conjecture

For the dihedral group D8 in characteristic two, the paper constructs a five-dimensional submodule U of a six-dimensional module V with Noether number 6 for U but 5 for V. Inflation extends the construction to groups admitting D8 as a quotient.

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Stable ID: math-wehlau-noether-number-counterexample-2026
Revision: math-wehlau-noether-number-counterexample-2026.v1
Field: Mathematics · Invariant theory and representation theory
Evidence: Tier 1 · Peer reviewed: No
Record state: Provisional · Provisional counterexample
Last checked: 2026-07-29

AI role

No AI role was disclosed in the inspected manuscript. The paper includes Magma code for its computations.

Record details

Problem or result: Monotonicity of Noether numbers when a group submodule is included in a larger module
Authors: Muhammad Fazeel Anwar
Institutions: Sukkur IBA University
Result date: Preprint submitted July 20, 2026

Why it matters

The explicit example reverses the inequality proposed by Wehlau in a concrete modular invariant-theory setting.

Limits

This is a first-version preprint without located independent specialist assessment or peer review. The result is characteristic-specific, and the accompanying Magma calculations were not independently rerun in this cycle.

Sources

Primary: Muhammad Fazeel Anwar, A Counterexample to Wehlau's Conjecture on Noether Numbers

Correction and revision history

2026-07-23 — Prepared as a provisional tracker addition with the characteristic-two and computational-verification limits stated explicitly.

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