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Hurwitz generation in groups of types F4, E6 2E6, E7 and E8

Pierro, Emilio (2022) Hurwitz generation in groups of types F4, E6 2E6, E7 and E8. Journal of Group Theory, 25 (4). 753 - 780. ISSN 1433-5883

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Identification Number: 10.1515/jgth-2021-0115


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.

Item Type: Article
Official URL:
Additional Information: © 2022 The Author
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 25 Feb 2022 17:24
Last Modified: 16 May 2024 03:38

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