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THE (2,3)-GENERATION OF THE CLASSICAL SIMPLE GROUPS OF DIMENSIONS 6 AND 7

Part of: Linear algebraic groups and related topics Special aspects of infinite or finite groups

Published online by Cambridge University Press:  05 August 2015

MARCO ANTONIO PELLEGRINI
MARCO ANTONIO PELLEGRINI*
Affiliation:
Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, I-25121 Brescia, Italy email marcoantonio.pellegrini@unicatt.it
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Abstract

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In this paper, we prove that the finite simple groups $\text{PSp}_{6}(q)$, ${\rm\Omega}_{7}(q)$ and $\text{PSU}_{7}(q^{2})$ are $(2,3)$-generated for all $q$. In particular, this result completes the classification of the $(2,3)$-generated finite classical simple groups up to dimension 7.

Keywords

generationclassical groups

MSC classification

Primary: 20G40: Linear algebraic groups over finite fields
Secondary: 20F05: Generators, relations, and presentations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 61 - 72
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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