Maximal-elasticity length sets for families of two-groups of exponent eight

Henry Zweiman · September 9, 2026

Full paper in Markdown · PDF · LaTeX source

For a noncyclic group G = C2^a + C4^b + C8^c, the paper proves that every longest atom has signed-support minimum distance dividing three. This distance is one whenever a+c is not 1 mod 3, or whenever c=1. The latter condition allows arbitrary numbers of order-two and order-four factors. For these families, maximal-elasticity length sets in transfer Krull monoids have an interval as their central part, with uniformly bounded exceptional ends.

The six-page manuscript gives universal hand proofs, including the signed-support classification and the group-algebra argument that excludes residual order-two terms. The general exponent-eight case remains unresolved.

Source and significance assessment · Internal proof review · Finite check results

Run python3 check.py to reproduce the 4,756 exact witness-atom checks. Complete Markdown was checked against the LaTeX source and its equations were rendered without errors. All six final PDF pages were visually inspected.

This is an AI-generated, internally checked proposed research result. Historical priority and outside mathematical verification remain provisional; no peer review, journal acceptance, or guaranteed citation impact is claimed. The manuscript and its two parameter families count as one paper in the public inventory.