Geometry & Topology Volume 8, issue 2 (2004)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Finiteness properties of soluble arithmetic groups over global function fields

Kai-Uwe Bux

Geometry & Topology 8 (2004) 611–644

DOI: 10.2140/gt.2004.8.611

Bibliography

1	H Abels, Finite presentability of S–arithmetic groups. Compact presentability of solvable groups, 1261, Springer (1987) MR903449
2	H Abels, K S Brown, Finiteness properties of solvable S–arithmetic groups : an example, from: "Proceedings of the Northwestern conference on cohomology of groups (Evanston, Ill., 1985)" (1987) 77 MR885096
3	H Abels, A Tiemeyer, Compactness properties of locally compact groups, Transform. Groups 2 (1997) 119 MR1451359
4	H Åberg, Bieri–Strebel valuations (of finite rank), Proc. London Math. Soc. (3) 52 (1986) 269 MR818928
5	P Abramenko, Chevalleygruppen, manuscript, Frankfurt (1994)
6	P Abramenko, Twin buildings and applications to S-arithmetic groups, 1641, Springer (1996) MR1624276
7	G Baumslag, W W Boone, B H Neumann, Some unsolvable problems about elements and subgroups of groups, Math. Scand. 7 (1959) 191 MR0163948
8	H Behr, Endliche Erzeugbarkeit arithmetischer Gruppen über Funktionenkörpern, Invent. Math. 7 (1969) 1 MR0238853
9	H Behr, Arithmetic groups over function fields: A complete characterization of finitely generated and finitely presented arithmetic subgroups of reductive algebraic groups, preprint 92–033, SFB 343, Bielefield (1992) MR1603845
10	H Behr, Arithmetic groups over function fields I : A complete characterization of finitely generated and finitely presented arithmetic subgroups of reductive algebraic groups, J. Reine Angew. Math. 495 (1998) 79 MR1603845
11	M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
12	R Bieri, Finiteness length and connectivity length for groups, from: "Geometric group theory down under (Canberra, 1996)", de Gruyter (1999) 9 MR1714837
13	R Bieri, B Eckmann, Finiteness properties of duality groups, Comment. Math. Helv. 49 (1974) 74 MR0340450
14	R Bieri, R Geoghegan, Connectivity properties of group actions on non-positively curved spaces, Mem. Amer. Math. Soc. 161 (2003) MR1950396
15	R Bieri, B Renz, Valuations on free resolutions and higher geometric invariants of groups, Comment. Math. Helv. 63 (1988) 464 MR960770
16	R Bieri, R Strebel, Valuations and finitely presented metabelian groups, Proc. London Math. Soc. (3) 41 (1980) 439 MR591649
17	A Borel, Linear algebraic groups, 126, Springer (1991) MR1102012
18	A Borel, J P Serre, Cohomologie d’immeubles et de groupes S–arithmétiques, Topology 15 (1976) 211 MR0447474
19	K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
20	K S Brown, Finiteness properties of groups, from: "Proceedings of the Northwestern conference on cohomology of groups (Evanston, Ill., 1985)" (1987) 45 MR885095
21	K S Brown, Buildings, Springer (1989) MR969123
22	F Bruhat, J Tits, Groupes réductifs sur un corps local, Inst. Hautes Études Sci. Publ. Math. (1972) 5 MR0327923
23	F Bruhat, J Tits, Groupes réductifs sur un corps local II : Schémas en groupes. Existence d’une donnée radicielle valuée, Inst. Hautes Études Sci. Publ. Math. (1984) 197 MR756316
24	K U Bux, Finiteness properties of certain metabelian arithmetic groups in the function field case, Proc. London Math. Soc. (3) 75 (1997) 308 MR1455858
25	K U Bux, Endlichkeitseigenschaften auflösbarer arithmetischer Gruppen über Funktionenkörpern, PhD thesis, Frankfurt (1997)
26	K U Bux, Finiteness properties of soluble S–arithmetic groups : a survey, from: "Groups: topological, combinatorial and arithmetic aspects", London Math. Soc. Lecture Note Ser. 311, Cambridge Univ. Press (2004) 64 MR2073347
27	, Algebraic number theory, , Academic Press (1967) MR0215665
28	C Chevalley, Certains schémas de groupes semi-simples, from: "Séminaire Bourbaki, Vol. 6", Soc. Math. France (1995) 219 MR1611814
29	, Group theory, Academic Press [Harcourt Brace Jovanovich Publishers] (1984) MR780565
30	D H Kochloukova, The FP_m–conjecture for a class of metabelian groups, J. Algebra 184 (1996) 1175 MR1407892
31	H Meinert, The homological invariants for metabelian groups of finite Prüfer rank : a proof of the Σ^m–conjecture, Proc. London Math. Soc. (3) 72 (1996) 385 MR1367084
32	H Meinert, Actions on 2–complexes and the homotopical invariant Σ² of a group, J. Pure Appl. Algebra 119 (1997) 297 MR1453518
33	B H Neumann, Some remarks on infinite groups, J. London. Math. Soc. 12 (1937) 120
34	B Renz, Geometrische Invarianten und Endlichkeitseigenschaften von Gruppen, PhD thesis, Frankfurt (1988)
35	M Ronan, Lectures on buildings, 7, Academic Press (1989) MR1005533
36	J P Serre, Trees, Springer (1980) MR607504
37	R Steinberg, Lectures on Chevalley groups, mimeographed notes, Yale University (1967)
38	R Strebel, Finitely presented soluble groups, from: "Group theory", Academic Press (1984) 257 MR780572
39	U Stuhler, Zur Frage der endlichen Präsentierbarkeit gewisser arithmetischer Gruppen im Funktionenkörperfall, Math. Ann. 224 (1976) 217 MR0419631
40	U Stuhler, Homological properties of certain arithmetic groups in the function field case, Invent. Math. 57 (1980) 263 MR568936
41	A Tiemeyer, A local-global principle for finiteness properties of S–arithmetic groups over number fields, Transform. Groups 2 (1997) 215 MR1451365
42	J Tits, Uniqueness and presentation of Kac–Moody groups over fields, J. Algebra 105 (1987) 542 MR873684
43	C T C Wall, Finiteness conditions for CW–complexes, Ann. of Math. (2) 81 (1965) 56 MR0171284
44	C T C Wall, Homological group theory, 36, Cambridge University Press (1979) MR564417
45	A Weil, Basic number theory, , Springer (1995) MR1344916