Title of article :
THE (p; q; r)-GENERATIONS OF THE SYMPLECTIC GROUP Sp(6; 2)
Author/Authors :
Mohammed Basheer, Ayoub Basheer School of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga, South Africa , Motalane, Malebogo J School of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga, South Africa , Seretlo, Thekiso T School of Mathematical and Computer Sciences University of Limpopo (Turfloop) Sovenga, South Africa
Abstract :
A nite group G is called (l; m; n)-generated, if it is a quotient group of the
triangle group T(l; m; n) =
⟨
x; y; zjxl = ym = zn = xyz = 1
⟩
: In [29], Moori posed the ques-
tion of nding all the (p; q; r) triples, where p; q and r are prime numbers, such that a
non-abelian nite 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 nite group
representations [33] are used in our computations.
Keywords :
Conjugacy classes , generation , simple groups , structure constants
Journal title :
Journal of Algebraic Structures and Their Applications
