Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



The cohomology of the groups of order $ 32$

Author: David J. Rusin
Journal: Math. Comp. 53 (1989), 359-385
MSC: Primary 20J06
MathSciNet review: 968153
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We have calculated the $ \bmod$-$ 2$ cohomology rings of all the groups of 32 elements. This paper describes the methods of calculation; the computer routines used can be adapted to assist in the calculation of the modular cohomology rings of other finite groups. We also describe the results of the calculations; the data we have collected provide a substantial increase in the supply of completed calculations in group cohomology, and so we take this opportunity to compare known results and open conjectures.

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

  • [1] M. F. Atiyah, "Characters and cohomology of finite groups," Publ. Math. Inst. Hautes Etudes Sci., v. 9, 1961, pp. 23-64. MR 0148722 (26:6228)
  • [2] H. Cartan & S. Eilenberg, Homological Algebra, Princeton Univ. Press, Princeton, NJ, 1956. MR 0077480 (17:1040e)
  • [3] J. Duflot, "Depth and equivariant cohomology," Comment. Math. Helv., v. 56, 1981, pp. 627-637. MR 656216 (83g:57029)
  • [4] L. Evens & S. Priddy, (unpublished).
  • [5] M. Feshbach & S. Priddy, "Stable splittings associated with Chevalley groups," J. Pure Appl. Algebra. (To appear.)
  • [6] Z. Fiedorowicz & S. Priddy, Homology of Classical Groups Over Finite Fields, Lecture Notes in Math., vol. 674, Springer-Verlag, Berlin and New York, 1978. MR 513424 (80g:55018)
  • [7] M. Hall & J. K. Senior, The Groups of Order $ {2^n}\;(n \leq 6)$, Macmillan, New York, 1964. MR 0168631 (29:5889)
  • [8] P. Hilton & U. Stammbach, A Course in Homological Algebra, Springer, New York, 1971. MR 0346025 (49:10751)
  • [9] D. Quillen, "The spectrum of an equivariant cohomology ring, I and II," Ann. of Math., v. 94, 1971, pp. 549-602. MR 0298694 (45:7743)
  • [10] D. Quillen, "The $ \bmod$-$ 2$ cohomology of extraspecial 2-groups and the spinor groups," Math. Ann., v. 194, 1971, pp. 197-212. MR 0290401 (44:7582)
  • [11] D. Rusin, The Cohomology of Groups Generated by Involutions, Thesis, Univ. of Chicago, 1984.
  • [12] D. Rusin, "The $ \bmod$-$ 2$ cohomology of metacyclic 2-groups," J. Pure Appl. Algebra, v. 44, 1987, pp. 315-327. MR 885115 (88k:20076)
  • [13] D. Rusin, "The kernel of the inflation map in group cohomology," J. Pure Appl. Algebra. (To appear.)
  • [14] D. Rusin, "Kernels of the restriction map in group cohomology," J. Pure Appl. Algebra. (To appear.) MR 1163289 (93j:20101)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 20J06

Retrieve articles in all journals with MSC: 20J06

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society