A necessary condition for an elliptic element to belong to a uniform tree lattice

Author:
Ying-Sheng Liu

Journal:
Proc. Amer. Math. Soc. **120** (1994), 1035-1039

MSC:
Primary 05C25; Secondary 05C05

DOI:
https://doi.org/10.1090/S0002-9939-1994-1203988-1

MathSciNet review:
1203988

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Abstract: Let be a universal cover of a finite connected graph, , and a group acting discretely and cocompactly on , i.e., a uniform lattice on . We give a necessary condition for an elliptic element of to belong to a uniform lattice or to the commensurability group. By using this condition, we construct some explicit examples.

**[AB]**R. Alperin and H. Bass,*Length functions of group actions on*-*trees*, Combinatorial Group Theory and Topology, Ann. of Math. Stud., no. 111, Princeton Univ. Press, Princeton, NJ, 1987, pp. 265-378. MR**895622 (89c:20057)****[B1]**H. Bass,*Covering theory for graphs of groups*, J. Pure Appl. Algebra (to appear). MR**1239551 (94j:20028)****[B2]**-,*Group actions on non-archimedean trees*, Aboreal Group Theory (Roger C. Alperin, ed.), Math. Sci. Res. Inst. Publ., vol. 19, Springer-Verlag, New York, 1988, pp. 69-131. MR**1105330 (93d:57003)****[BK]**H. Bass and R. Kulkarni,*Uniform tree lattices*, J. Amer. Math. Soc.**3**(1990), 843-902. MR**1065928 (91k:20034)****[K]**R. Kulkarni,*Lattices on trees, automorphism of graphs, free groups, surfaces*, preprint, CUNY, September 1988.**[KPS]**A. Karass, A. Pietrowski, and D. Solitar,*Finite and infinite cyclic extensions of free groups*, Australian Math. Soc.**16**(1973), 458-466. MR**0349850 (50:2343)****[L1]**Y. Liu,*Density of commensurability groups of uniform tree lattices*, J. Algebra (to appear). MR**1273278 (95c:20036)****[L2]**-,*Commensurability groups of uniform tree lattices*, Columbia Univ. Dissertation, 1991.**[Lub]**A. Lubotzky,*Trees and discrete subgroups of Lie groups over local fields*, Bull. Amer. Math. Soc. (N.S.)**20**(1988), 27-31. MR**945301 (89g:22016)****[SP]**J.-P. Serre,*Trees*, Springer-Verlag, New York, 1980. MR**607504 (82c:20083)**

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1203988-1

Article copyright:
© Copyright 1994
American Mathematical Society