On the Simple Sporadic Group He Generated by the (2,3,t) Generators

A group G is said to be (2,3,t)-generated if it can be generated by two elements x and y such that o (x)=2, o(y)=3 and o(xy)=t. In the present article, we investigate (2,3,t)-generations for the Held s sporadic simple group He, where t is a divisor of |He|. Most of the computations were carried out with the aid of computer algebra system GAP [23].