An identification theorem for groups with socle \(\mathrm{PSU}_6(2)\).
The authors provide a 3-local characterization of the almost simple groups with socle \(\mathrm{PSU}_6(2)\). The first author in earlier work [J. Algebra 300, No. 2, 707-728 (2006; Zbl 1102.20013)] obtained a partial result in this direction. The full result will be applied in a larger project which began by \textit{U. Meierfrankenfeld, B. Stellmacher} and \textit{G. Stroth} [``The structure theorem for finite groups with a large \(p\)-subgroup'', preprint (2011)] and aims to provide an alternative proof for some major parts of the classification of the finite simple groups. The group \(\mathrm{PSU}_6(2)\) is a Lie type group defined in characteristic 2 and so its appearance in a setting where 3 is the significant prime is unusual.
scientific article; zbMATH DE number 6189297
scientific article