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A remark on a theorem of J. Tits


Authors: Curtis D. Bennett and Sergey Shpectorov
Journal: Proc. Amer. Math. Soc. 129 (2001), 2571-2579
MSC (1991): Primary 20E42, 20D06, 51E12, 51E24
Published electronically: February 9, 2001
MathSciNet review: 1838379
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Abstract:

Let $G$ be a rank two Chevalley group and $\Gamma$ be the corresponding Moufang polygon. J. Tits proved that $G$ is the universal completion of the amalgam formed by three subgroups of $G$: the stabilizer $P_1$of a point $a$ of $\Gamma$, the stabilizer $P_2$ of a line $\ell$ incident with $a$, and the stabilizer $N$ of an apartment $A$ passing through $a$ and $\ell$. We prove a slightly stronger result, in which the exact structure of $N$ is not required. Our result can be used in conjunction with the ``weak $BN$-pair" theorem of Delgado and Stellmacher in order to identify subgroups of finite groups generated by minimal parabolics.


References [Enhancements On Off] (What's this?)

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Additional Information

Curtis D. Bennett
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email: cbennet@bgnet.bgsu.edu

Sergey Shpectorov
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email: sergey@bayes.bgsu.edu

DOI: https://doi.org/10.1090/S0002-9939-01-05940-8
Received by editor(s): January 24, 2000
Published electronically: February 9, 2001
Additional Notes: The second author received partial support from NSF grant #9896154.
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2001 American Mathematical Society