The $(p,q,r)$-generations of the symplectic group $Sp(6,2)$

Document Type : Research Paper

Authors

School of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga 0727, South Africa.

Abstract

A finite group $G$ is called \textit{$(l,m, n)$-generated}, if it is a quotient group of the triangle group $T(l,m, n) = \left<x, y, z|x^{l} = y^{m} = z^{n} = xyz = 1\right>.$ In 29, Moori posed the question of finding all the $(p,q,r)$ triples, where $p,\ q$ and $r$ are prime numbers, such that a non-abelian finite simple group $G$ is a $(p,q,r)$-generated. In this paper we establish all the $(p,q,r)$-generations of the symplectic group $Sp(6,2).$ GAP 20 and the Atlas of finite group representations 33 are used in our computations.

Keywords

References

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Algebraic Structures and Their Applications
Volume 8, Issue 2
August 2021
Pages 31-49

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