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THE $(2,3)$-GENERATION OF THE SPECIAL LINEAR GROUPS OVER FINITE FIELDS

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

Published online by Cambridge University Press:  26 September 2016

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

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We complete the classification of the finite special linear groups $\text{SL}_{n}(q)$ which are $(2,3)$-generated, that is, which are generated by an involution and an element of order $3$. This also gives the classification of the finite simple groups $\text{PSL}_{n}(q)$ which are $(2,3)$-generated.

Keywords

generationlinear 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 95 , Issue 1 , February 2017 , pp. 48 - 53
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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