Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Duality and local group cohomology

Author: P. R. Hewitt
Journal: Proc. Amer. Math. Soc. 126 (1998), 1909-1914
MSC (1991): Primary 20J05
MathSciNet review: 1468193
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be a group, let $k$ be a field, and let ${\mathcal{L}}$ be a local system - an upwardly directed collection of subgroups whose union is $G$. In this paper we give a short, elementary proof of the following result: If either $A$ is a $k$-$kG$-bimodule, or else $k$ is finite dimensional over its center, then $\operatorname{Ext}^{*}_{G}(A,B^{\vee }) =\varprojlim _{L\in\mathcal{L}} \operatorname{Ext}^{*}_{L}(A,B^{\vee })$. From this we deduce as easy corollaries some recent results of Meierfrankenfeld and Wehrfritz on the cohomology of a finitary module.

References [Enhancements On Off] (What's this?)

  • [AM] A Adem, J Milgram, Cohomology of Finite Groups, Springer-Verlag, 1994. MR 96f:20082
  • [B] D Benson, Representations and Cohomology I, Cambridge University Press, 1991. MR 92m:20005
  • [CPS] E Cline, B Parshall, L Scott, Cohomology of finite groups of Lie type, I, Publ Math IHES 45 (1975), 169-191. MR 53:3134
  • [M] U Meierfrankenfeld, A note on the cohomology of finitary modules, Proc AMS (to appear).
  • [Ph] R Phillips, Finitary linear groups: a survey, Finite and Locally Finite Groups, Kluwer Academic Publishers, 1995, pp. 111-146. MR 96m:20080
  • [ShW] M Shirvani, B Wehrfritz, Skew Linear Groups, Cambridge University Press, 1986. MR 89h:20001
  • [S] E Spanier, Algebraic Topology, McGraw-Hill, 1966. MR 35:1007
  • [W-1] B Wehrfritz, Complete reducibility in skew linear groups, Jour LMS 28 (1983), 301-309. MR 85g:20020
  • [W-2] B Wehrfritz, The complete reducibility of locally completely reducible finitary linear groups, Bull LMS 29 (1997), 173-176. CMP 97:06

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20J05

Retrieve articles in all journals with MSC (1991): 20J05

Additional Information

P. R. Hewitt
Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606

Received by editor(s): December 12, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society