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)

 
 

 

The complexity of a module and elementary abelian subgroups: a geometric approach


Author: Peter Symonds
Journal: Proc. Amer. Math. Soc. 113 (1991), 27-29
MSC: Primary 20J06; Secondary 20C20
DOI: https://doi.org/10.1090/S0002-9939-1991-1062838-4
MathSciNet review: 1062838
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We present a proof of the theorem of Alperin and Evens that the complexity of a module is determined by the complexities of its restrictions to elementary abelian subgroups. We use only well-known properties of the spectral sequence.


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

  • [AE] J. L. Alperin and L. Evens, Representations, resolutions and Quillen's dimension theorem, J. Pure Appl. Algebra 26 (1981), 1-9. MR 621284 (82j:20020)
  • [B] K. S. Brown, Cohomology of groups, Springer-Verlag, New York, 1982. MR 672956 (83k:20002)
  • [C] J. F. Carlson, Restrictions of modules over modular group algebras, J. Algebra 53 (1978), 334-343. MR 0491914 (58:11089)
  • [D] A. Dold, Relations between ordinary and extraordinary homology, Algebraic Topology, Student's Guide (J. F. Adams, ed.), London Math. Soc. Lecture Note Ser., No. 4, Cambridge Univ. Press, London and New York, 1972.
  • [H] D. Husemoller, Fibre bundles 2nd ed., Springer-Verlag, New York, 1975. MR 0370578 (51:6805)
  • [S] J.-P. Serre, Sur la dimension cohomologique des groupes profinis, Topology 3 (1965), 413-420. MR 0180619 (31:4853)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20J06, 20C20

Retrieve articles in all journals with MSC: 20J06, 20C20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1062838-4
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society