The (p; q; r)-generations of the alternating group A10

Abstract

A nite group G is said to be (l; m; n)-generated, if it is a quotient group of the triangle group T(l; m; n) = ⟨ x; y; zlx^l = y^m = zⁿ = xyz = 1⟩ : In [28], Moori posed the question 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 (p; q; r)- generated. In this paper we will establish all the (p; q; r)-generations of the alternating group A10: GAP [24] and the Atlas of nite group representations [1] are used in our computations.

Key words: Conjugacy classes, generation, structure constant, alternating groups.