Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-08-01T10:24:08.743Z Has data issue: false hasContentIssue false

On the vanishing of twisted nil groups

Published online by Cambridge University Press:  23 July 2008

Daniel Juan-Pineda
Affiliation:
Instituto de Matemáticas, Unidad Morelia. Universidad Nacional Autónoma de México Campus Morelia, Apartado Postal 61-3 (Xangari), Morelia, Michoacán, MEXICO 58089, daniel@matmor.unam.mx.
Rafael Ramos
Affiliation:
Instituto de Matemáticas, Unidad Morelia. Universidad Nacional Autónoma de México Campus Morelia, Apartado Postal 61-3 (Xangari), Morelia, Michoacán, MEXICO 58089, rramos@matmor.unam.mx.
Get access

Abstract

Let G be a finite group and [G] its integral group ring. We prove that the twisted nil groups N([G]) vanish for all i ≤ 1 for G a finite group of square-free order.

Type
Research Article
Copyright
Copyright © ISOPP 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bartels, A. C., On the domain of the assembly map in algebraic K-theory, Algebr. Geom. Topol. 3 (2003), 10371050CrossRefGoogle Scholar
2.Bartels, A. C., Farrell, T., Jones, L. and Reich, H.On the Isomorphism Conjecture in algebraic K-Theory, Topology 43 (2004), 157213CrossRefGoogle Scholar
3.Bass, H., Algebraic K-Theory, W.A. Benjamin, Inc., New York, 1968Google Scholar
4.Davis, J.F. and Lück, W., Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory, K-Theory 15 (1998), 201252CrossRefGoogle Scholar
5.F. T., The nonfiniteness of Nil, Proc. Amr. Math. Soc. 65 (1977), 215216Google Scholar
6.Farrell, F.T. and Hsiang, W.-c., A formula for K1Rα[T], Proc. Symp. Pure Math. vol. 17, Applications of Categorical Algebra, American Mathematical Society, Providence, 1970Google Scholar
7.Farrell, F. T. ; Hsiang, W. C.The Whitehead group of poly-(finite or cyclic) groups, J. London Math. Soc. (2) 24 no. 2 (1981), 308324CrossRefGoogle Scholar
8.Farrell, F. T. and Jones, L.The lower algebraic K-Theory of virtually infinite cyclic groups K- Theory 9 (1995), 1330CrossRefGoogle Scholar
9.Farrell, F.T. and Jones, L., Isomorphism conjectures in algebraic K-theory, J. Amer. Math. Soc. 6 (2) (1993), 249298Google Scholar
10.Grunewald, J., The Behavior of Nil-Groups under Localization Doctoral Dissertation, Münster, Germany 2005Google Scholar
11.Guin-Waléry, D. and Loday, J. L., Obstruction à l'excision en K-théorie algébrique. In Algebraic K-theory, Evanston 1980 (Proc. Conf. Northwestern Univ. Evanston, Ill., 1980), Lecture Notes in Math. 854, 179-216Springer, Berlin, 1981Google Scholar
12.Harmon, D. R., NK1 of finite groups, Proc. of the Amer. Math. Soc. 100 (2) (1987), 229232Google Scholar
13.Ireland, K. and Rosen, M., A classical introduction to modern number theory Springer, GTM 84, 1990CrossRefGoogle Scholar
14.Juan-Pineda, D. and Leary, I. J.On Classifying spaces for the family of virtually cyclic subgroups, Contemporary Mathematics of the AMS 407 (2006), 135145CrossRefGoogle Scholar
15.Lafont, J. F. and Ortiz, I., Relating the Farrell Nil-groups with the Waldhausen Nil-groups, to appear in Math. ForumGoogle Scholar
16.Martin, R., PhD. Dissertation, Columbia University, 1975Google Scholar
17.Munkholm, H. and Prassidis, S., On the exponent of the cokernel of the forget-control map on NK0 groups, Fund. Math. 172 (2002), 201216Google Scholar
18.Quillen, D., Higher Algebraic K-Theory: I, LNM 341, Springer-Verlag, 1973Google Scholar
19.Ramos, R., Grupos Nil torcidos en Teoría K-algebraica, Doctoral Dissertation, Facultad de Ciencias, Universidad Nacional Autónoma de México, 2006Google Scholar
20.Quinn, F., Hyperelementary assembly for K-theory of virtually abelian groups. arXiv:math.KT/0509294v4, 2006Google Scholar
21.Rim, D. S., Modules over finite groups, Ann. of Math. 69 (2) (1959), 700712Google Scholar