Papers › Hurwitz Generation in Groups of Types F₄, E₆, ²E₆, E₇ and E₈
Hurwitz Generation in Groups of Types F₄, E₆, ²E₆, E₇ and E₈
Emilio Pierro
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
A Hurwitz generating triple for a group G is an ordered triple of elements (x,y,z) ∈G³ where x²=y³=z⁷=xyz=1 and ⟨x,y,z ⟩= G. For the finite quasisimple exceptional groups of types F₄, E₆, ²E₆, E₇ and E₈, we provide restrictions on which conjugacy classes x, y and z can belong to if (x,y,z) is a Hurwitz generating triple. We prove that there exist Hurwitz generating triples for F₄(3), F₄(5), F₄(7), F₄(8), E₆(3) and E₇(2), and that there are no such triples for F₄(2³ⁿ⁻²), F₄(2³ⁿ⁻¹), E₆(7³ⁿ⁻²), E₆(7³ⁿ⁻¹), SE₆(7ⁿ) or ²E₆(7ⁿ) when n ≥1.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections