Twin trees and -gons
Author: Curtis D. Bennett
Journal: Trans. Amer. Math. Soc. 349 (1997), 2069-2084
MSC (1991): Primary 51E12, 20E99
MathSciNet review: 1370635
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Abstract: We define a natural generalization of generalized -gons to the case of -graphs (where is a totally ordered abelian group and ). We term these objects -gons. We then show that twin trees as defined by Ronan and Tits can be viewed as -gons, where is ordered lexicographically. This allows us to then generalize twin trees to the case of -trees. Finally, we give a free construction of -gons in the cases where is discrete and has a subgroup of index that does not contain the minimal element of .
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Curtis D. Bennett
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Keywords: $\Lambda$-trees, twin trees, generalized $n$-gons
Received by editor(s): April 24, 1994
Received by editor(s) in revised form: January 4, 1996
Additional Notes: The author gratefully acknowledges the support of an NSF postdoctoral fellowship.
Article copyright: © Copyright 1997 American Mathematical Society