Generators and relations for the Lyons sporadic simple group (Q1348967)

A new presentation for the sporadic simple Lyons group \(Ly\) is produced by producing presentations for each of the groups of an \(Ly\)-amalgam, say \(\mathcal A\), and applying the characterization of \(Ly\) as the universal completion of \(\mathcal A\). The latter characterization is computer-free, whereas the verifications of the presentations for the groups belonging to \(\mathcal A\) involve computer calculations. Furthermore, words in the standard generators for \(Ly\) are given which deliver a set of elements satisfying the new presentation and can be used to decide whether a group suspected to be the Lyons group is in fact isomorphic to \(Ly\).