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

Basheer, Ayoub; Motalane, Malebogo John; Seretlo, Thekiso Trevor

doi:10.22034/as.2021.1975

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

Document Type : Research Paper

Authors

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

10.22034/as.2021.1975

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) = ⟨ x, y, z | x^{l} = y^{m} = z^{n} = x y z = 1 ⟩ .

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

S p (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

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

References

Volume 8, Issue 2
August 2021
Pages 31-49

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

References

Volume 8, Issue 2August 2021Pages 31-49

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How to cite

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

Volume 8, Issue 2
August 2021
Pages 31-49