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2 results

Local identification of spherical buildings and finite simple groups of Lie type
ULRICH MEIERFRANKENFELD, GERNOT STROTH, RICHARD M. WEISS
Journal:

Mathematical Proceedings of the Cambridge Philosophical Society / Volume 154 / Issue 3 / May 2013

Published online by Cambridge University Press:

07 February 2013, pp. 527-547

Print publication:

May 2013
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We give a short proof of the uniqueness of finite spherical buildings of rank at least 3 in terms of the structure of the rank 2 residues and use this result to prove a result making it possible to identify an arbitrary finite group of Lie type from knowledge of its “parabolic structure” alone. Our proof also involves a connection between loops, “Latin chamber systems” and buildings.

AN IDENTIFICATION THEOREM FOR GROUPS WITH SOCLE PSU${}_{6} (2)$
Part of
- Representation theory of groups
CHRIS PARKER, GERNOT STROTH
Journal:

Journal of the Australian Mathematical Society / Volume 93 / Issue 3 / December 2012

Published online by Cambridge University Press:

25 February 2013, pp. 277-310

Print publication:

December 2012
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We identify the groups ${\text{PSU} }_{6} (2)$, ${\text{PSU} }_{6} (2){: }2$, ${\text{PSU} }_{6} (2){: }3$ and $\text{Aut} ({\text{PSU} }_{6} (2))$ from the structure of the centralizer of an element of order three.