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

Pierro, Emilio ORCID: 0000-0003-1300-7984 (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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Abstract

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:	https://www.degruyter.com/journal/key/jgth/html
Additional Information:	© 2022 The Author
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	25 Feb 2022 17:24
Last Modified:	17 Oct 2024 16:43
URI:	http://eprints.lse.ac.uk/id/eprint/113844

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