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

Document Type : Original Article


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



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.