Local characteristic $p$ completions of weak $bn$-pairs

• Autores: Christopher Parker, Peter Rowley
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 93, Nº 2, 2006, págs. 325-394
• Idioma: inglés
• DOI: 10.1112/s0024611506015802
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• Resumen

  • This paper establishes recognition theorems for the finite Lie-type groups defined in odd characteristic $p$. The hypotheses of these theorems are couched in terms of certain local data in the form of an amalgam which is called a weak $BN$-pair of rank 2. The groups to be recognized are completions of these amalgams which satisfy the condition of being of local characteristic $p$ (a condition satisfied by the finite Lie-type groups defined in characteristic $p$). The results presented will find application in one of the ongoing revisions of the finite simple group classification.