A 3-local identification of two almost simple extensions of \(P\Omega_8^+(2)\).
For a prime \(p\), a finite group \(G\) is of parabolic characteristic \(p\) if \(C_H(O_p(H))\leq O_p(H)\) for any \(p\)-local subgroup \(H\) of \(G\) where \(H\) contains a Sylow \(p\)-subgroup of \(G\). There exists a project of the study of groups of parabolic characteristic \(p\) [see \textit{U. Meierfrankenfeld, B. Stellmacher} and \textit{G. Stroth}, in Groups, combinatorics and geometry. Proceedings of the L.M.S. Durham symposium, Durham 2001. River Edge: World Scientific. 155-192 (2003; Zbl 1031.20008)]. The author provides a 3-local characterization of the almost simple groups of parabolic characteristic 3 of shapes \(P\Omega^+_8(2).3\) and \(P\Omega^+_8(2).\text{Sym}(3)\) (the simple group \(P\Omega^+_8(2)\) is not of parabolic characteristic 3). This result is used by \textit{C. Parker} and \textit{G. Stroth} [A characterization of \(^2E_6(2)\), \(Fi_{22}\) and \(\Aut(Fi_{22})\) from a characteristic 3 perspective. Preprint (2010)] for the 3-local characterization of the other such group namely \(^2E_6(2)\).
groups of parabolic characteristic \(p\)
scientific article; zbMATH DE number 5888497