Order 49 = 7²
1 / 2 paper-excluded 0 / 2 Lean-excluded odd candidate
Why a candidate
Order 49 = 7² is a candidate because it divides the following Theorem 6 maxima: 147.
From the paper (Macaj–Siran 2010)
Lemma 19 case (5) says: an automorphism subgroup of
order 7² must be isomorphic to ℤ₇ × ℤ₇
(with Fix an edge). The cyclic case ℤ₄₉
is therefore paper-excluded.
Group classification
| SmallGroup | Group | Description | Paper | Lean |
|---|---|---|---|---|
(49, 1) | ℤ₄₉ | Cyclic group of order 49. | excluded (Lemma 19) | open |
(49, 2) | ℤ₇ × ℤ₇ | Elementary abelian; the only possibility per Lemma 19 (Fix = edge). | allowed | open |
Project status
open — no natural-language proof or Lean formalization yet. See Contribute for pointers if you want to attack this case.