Presentations of some finite groups with applications to the O'Nan simple group
The author gives presentations for the groups \(S_ 5\), \(L_ 2(11)\), \(M_{11}\), \(M_{12}:2\), \(J_ 1\), and \(12\cdot L_ 3(4):2\) and presentations for groups G, H with \([H:G]=2\) which have \(3\cdot O'N\) resp. \(3\cdot O'N:2\) as epimorphic images. The generators represent involutions, the relations give the ''orders'' of the products of two generators as for Coxeter groups and are supplemented by further relations like \((bc)^ 2=a\) or \((abc)^ 5=1\). The proofs use coset enumeration by a computer with respect to a previously identified subgroup generated by some of the generators. The enumeration for \([H:G]=2\) needs space for 5000 cosets.
scientific article; zbMATH DE number 3995961