Artículos de revistas
More About The Geometric Invariants Σm(g) And Σm(g, ℤ) For Groups With Normal Locally Polycyclic-by-finite Subgroups
Registro en:
Mathematical Proceedings Of The Cambridge Philosophical Society. , v. 130, n. 2, p. 295 - 306, 2001.
3050041
2-s2.0-23044527511
Autor
Kochloukova D.H.
Institución
Resumen
The main result of the paper is that the real characters of a group G of type FPm (Fm respectively) that do not vanish on a normal locally polycyclic-by-finite subgroup represent elements of the geometric invariant Σm(G, ℤ) (Σm(G) respectively). In the case m = 2 a stronger result is proved. Some consequences of the main result are considered. © 2001 Cambridge Philosophical Society. 130 2 295 306 Aberg, H., Bieri-Strebel valuations (of finite rank) (1986) Proc. London Math. Soc., 52 (3), pp. 269-304 Bestvina, M., Brady, N., Morse theory and finiteness properties of groups (1997) Invent. Math., 129 (3), pp. 445-470 Bieri, R., Groves, J.R.J., The geometry of the set of characters induced by valuations (1984) J. Reine Angew. Math., 347, pp. 168-195 Bieri, R., Groves, J.R.J., Metabelian groups of type FP∞ are virtually of type FP (1982) Proc. London Math. Soc., 45 (3), pp. 365-384 Bieri, R., Newmann, W.D., Strebel, R., A geometric invariant of discrete groups (1987) Invent. Math., 90, pp. 451-477 Bieri, R., Renz, B., Valuations on free resolutions and higher geometric invariants of groups (1988) Comment. Math. Helv., 63, pp. 464-497 Bieri, R., Strebel, R., Valuations and finitely presented metabelian groups (1980) Proc. London Math. Soc., 41 (3), pp. 439-464 Gehrke, R., The higher geometric invariants for groups with sufficient commutativity (1998) Comm. in Algebra, 26 (4), pp. 1097-1115 Kochloukova, D.H., (1997) The FPm-conjecture for a Class of Metabelian Groups and Related Topics, , PhD Dissertation, University of Cambridge Kochloukova, D.H., The Σm-conjecture for a class of metabelian groups (1999) LMS Lecture Note Series 261, pp. 492-503. , Groups St Andrews '97 in Bath. Cambridge University Press Kochloukova, D.H., The Σ2-conjecture for metabelian groups and some new conjectures: The split extension case (1999) J. Algebra, 222 (2), pp. 357-375 Kochloukova, D.H., The FPm-conjecture for a class of metabelian groups (1996) J. Algebra, 184, pp. 1175-1204 Meinert, H., The homological invariants for metabelian groups of finite Prufer rank: A proof of the Σm-conjecture (1996) Proc. London Math. Soc., 72 (3), pp. 385-424 Meinert, H., Actions on 2-complexes and the homotopical invariant Σ2 of a group (1997) J. Pure Appl. Algebra., 119, pp. 297-317 Meier, J., Meinert, H., Vanwyk, L., Higher generation subgroup sets and the Σ-invariants of graph products (1998) Comment. Math. Helv., 73, pp. 22-44 Renz, B., (1988) Geometrische Invarianten und Endlichkeitseigenschaften von Gruppen, , Dissertation. Universität Frankfurt a.M Renz, B., Geometric invariants and H N N-extensions (1989) Proceedings of the Singapore Group Theory Conference, pp. 465-484. , Group theory June 1987 (ed. K. N. Cheng and Y. K. Leong) W. de Gruyter