Denote by e\*(L) and ~,(L) respectively the upper length and lower length of a finite lattice L. The lattice L is said to be uniform if for each integer k with e,(L) < k < Β’\*(L) there exists in L a maximal chain of length k. It is shown that the closed-set lattice of a finite graph G is uniform if
Density of the Commensurability Groups of Uniform Tree Lattices
β Scribed by Y.S. Liu
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 499 KB
- Volume
- 165
- Category
- Article
- ISSN
- 0021-8693
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β¦ Synopsis
Let (X) be a universal cover of a finite connected graph, and (\Gamma) a group acting discretely and cocompactly on (X), i.e., a uniform lattice on (X). We announce a proof of the conjecture of H. Bass and R. Kulkarni (J. Amer. Math. Soc. No. 4 (1990), 843-902) that the commensurability group of (\Gamma) is dense in the automorphism group of (X). 1994 Academic Press, Inc.
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97α108 proved a much stronger result, the strong independence of the automorphism group and the congruence lattice in the finite case. In this paper, we provide a full affirmative solution of the above problem. In fact, we prove much stronger results, verifying strong independence for general lattic