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LOCAL CHARACTERISTIC $p$ COMPLETIONS OF WEAK $BN$-PAIRS

Published online by Cambridge University Press:  07 August 2006

CHRISTOPHER PARKER  and
PETER ROWLEY
CHRISTOPHER PARKER
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United [email protected]
PETER ROWLEY
Affiliation:
School of Mathematics, University of Manchester, P.O. Box 88, Manchester, M60 1QD, United [email protected]
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Abstract

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.

Keywords

20D08
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 93 , Issue 2 , September 2006 , pp. 325 - 394
Copyright
2006 London Mathematical Society

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Footnotes

This work was partially supported by a London Mathematical Society scheme 4 grant.