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ON $(2, 3, n)$-GENERATIONS OF THE FISCHER GROUP $F i_{23}$
Keywords:
Fischer group $F i_{23}$ simple group, generating triple, sporadic group.DOI:
https://doi.org/10.17654/0972555524017Abstract
A finite group $G$ is called $(l, m, n)$-generated if $G$ can be generated by two elements $x$ and $y$ such that $o(x)=l, \quad o(y)=m$ and $o(x y)=n$. In [2], generating pairs of the Fischet group $F i_{23}$ was determined for all $(2,3, r)$ triples, where $r$ was a prime divisor of the order of $\mathrm{Fi}_{23}$. In the present article, we extend these results by assuming $r$ to be any odd divisor of $\left|F i_{23}\right|$. In particular, we determine all the $(2,3, n)$-generations for the Fischer's sporadic simple group $F i_{23}$, where $n$ is an odd divisor of $\left|F i_{23}\right|$.
Received: February 25, 2024
Accepted: April 8, 2024
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