Hurwitz Generation of PSp6(q)
M.C. Tamburini Bellani, Maxim Aleksandrovich Vsemirnov · Communications in Algebra · 2015
We show that the symplectic groups PSp6(q) are Hurwitz for all q = p m ≥ 5, with p an odd prime. The result cannot be improved since, for q even and q = 3, it is known that PSp6(q) is not Hurwitz. In particular, n = 6 turns out to be the smallest degree for which a family of classical simple groups of degree n, over 𝔽 p m , contains Hurwitz groups for infinitely many values of m. This fact, for a given (possibly large) p, also follows from [9 Larsen , M. , Lubotzky , A. , Marion , C. ( 2014 ). Deformation theory and finite simple quotients of triangle groups I . J. Eur. Math. Soc. (JEMS) 16 ( 7 ): 1349 – 1375 .[Crossref], [Web of Science ®] , [Google Scholar]] and [10 Larsen , M. , Lubotzky , A. , Marion , C. ( 2014 ). Deformation theory and finite simple quotients of triangle groups II . Groups Geom. Dyn. 8 ( 3 ): 811 – 836 .[Crossref], [Web of Science ®] , [Google Scholar]].