(2,3, t)-Generations for the janko group j₃

Abstract

A group G is (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 [8] the problem is posed to find all possible (l,m,n)-generations for the non-abelian finite simple groups. In this paper we partially answer this question for the Janko group J ₃. We find all (2, 3, t)-generations as well as (2, 2,2,p)-generations, p a prime, for J ₃