Volume 35 • Number 3 • 2012   • On the Simple Sporadic Group He Generated by the $(2,3,t)$ Generators Faryad Ali and Mohammed Ali Faya Ibrahim Abstract. 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 \textrm{He}, where $t$ is a divisor of $|\textrm{He}|$. Most of the computations were carried out with the aid of computer algebra system $\mathbb{GAP}$ [23]. 2010 Mathematics Subject Classification: 20D08, 20F05. Full text: PDF