The (p,q,r)-generations of the alternating group A_11

Document Type : Original Article

Authors

Ayoub Basheer Mohammed Basheer ¹

Malebogo Motalane ²

Thekiso Trevor Seretlo ³

¹ University of Limpopo

² University of Limpopo.

³ School of Mathematical and Computer Sciences, University of Limpopo (Turfloop), P Bag X1106, Sovenga 0727, South Africa

10.22034/kjm.2020.205718.1600

Abstract

A finite group G is called (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 = xyz = 1>. In [23], 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 alternating group A_11.$ GAP [14] and the Atlas of finite group representations[28] are used in our computations.

Keywords

Conjugacy classes

generation

simple groups

structure constants

alternating groups

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