Twin trees and -gons

Author:
Curtis D. Bennett

Journal:
Trans. Amer. Math. Soc. **349** (1997), 2069-2084

MSC (1991):
Primary 51E12, 20E99

DOI:
https://doi.org/10.1090/S0002-9947-97-01703-0

MathSciNet review:
1370635

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Curtis D. Bennett**

Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403

Email:
cbennet@andy.bgsu.edu

DOI:
https://doi.org/10.1090/S0002-9947-97-01703-0

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