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On the vanishing of twisted nil groups

Published online by Cambridge University Press:  23 July 2008

Daniel Juan-Pineda  and
Rafael Ramos
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, [email protected].
Rafael Ramos
Affiliation:
Instituto de Matemáticas, Unidad Morelia. Universidad Nacional Autónoma de México Campus Morelia, Apartado Postal 61-3 (Xangari), Morelia, Michoacán, MEXICO 58089, [email protected].
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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.

Keywords

K-theoryNil groups
Type
Research Article
Information
Journal of K-Theory , Volume 3 , Issue 1 , February 2009 , pp. 153 - 163
Copyright
Copyright © ISOPP 2009

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References

1.Bartels, A. C., On the domain of the assembly map in algebraic K-theory, Algebr. Geom. Topol. 3 (2003), 1037–1050CrossRefGoogle Scholar
2.Bartels, A. C., Farrell, T., Jones, L. and Reich, H.On the Isomorphism Conjecture in algebraic K-Theory, Topology 43 (2004), 157–213CrossRefGoogle 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), 201–252CrossRefGoogle Scholar
5.F. T., The nonfiniteness of Nil, Proc. Amr. Math. Soc. 65 (1977), 215–216Google 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), 308–324CrossRefGoogle Scholar
8.Farrell, F. T. and Jones, L.The lower algebraic K-Theory of virtually infinite cyclic groups K- Theory 9 (1995), 13–30CrossRefGoogle Scholar
9.Farrell, F.T. and Jones, L., Isomorphism conjectures in algebraic K-theory, J. Amer. Math. Soc. 6 (2) (1993), 249–298Google 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), 229–232Google 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), 135–145CrossRefGoogle 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), 201–216Google 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), 700–712Google Scholar