The complete classification of the finite simple groups that are (2, 3)-generated is a problem which is still open only for orthogonal groups. Here, we construct (2, 3)-generators for the finite odd-dimensional orthogonal groups O2k+1(q), k = 4. As a byproduct, we also obtain (2, 3)-generators for O+ 4k(q) with k = 3 and q odd, and for O± 4k+2(q) with k = 4 and q = ±1 (mod 4).
Pellegrini, M. A., Tamburini Bellani, M. C., THE (2, 3)-GENERATION OF THE FINITE SIMPLE ODD-DIMENSIONAL ORTHOGONAL GROUPS, <<JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY>>, 2024; (117): 130-148. [doi:10.1017/S1446788724000016] [https://hdl.handle.net/10807/268100]
THE (2, 3)-GENERATION OF THE FINITE SIMPLE ODD-DIMENSIONAL ORTHOGONAL GROUPS
Pellegrini, Marco Antonio
Primo
;
2024
Abstract
The complete classification of the finite simple groups that are (2, 3)-generated is a problem which is still open only for orthogonal groups. Here, we construct (2, 3)-generators for the finite odd-dimensional orthogonal groups O2k+1(q), k = 4. As a byproduct, we also obtain (2, 3)-generators for O+ 4k(q) with k = 3 and q odd, and for O± 4k+2(q) with k = 4 and q = ±1 (mod 4).
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