The cohomology of the groups of order
Author:
David J. Rusin
Journal:
Math. Comp. 53 (1989), 359385
MSC:
Primary 20J06
MathSciNet review:
968153
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Abstract: We have calculated the  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.
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D. Rusin, "The kernel of the inflation map in group cohomology," J. Pure Appl. Algebra. (To appear.)
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David
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 M. F. Atiyah, "Characters and cohomology of finite groups," Publ. Math. Inst. Hautes Etudes Sci., v. 9, 1961, pp. 2364. 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. 627637. 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 L. Evens & S. Priddy, (unpublished).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, SpringerVerlag, Berlin and New York, 1978. MR 513424 (80g:55018)
 [7]
 M. Hall & J. K. Senior, The Groups of Order , Macmillan, New York, 1964. MR 0168631 (29:5889)
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 P. Hilton & U. Stammbach, A Course in Homological Algebra, Springer, New York, 1971. MR 0346025 (49:10751)
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 D. Quillen, "The spectrum of an equivariant cohomology ring, I and II," Ann. of Math., v. 94, 1971, pp. 549602. MR 0298694 (45:7743)
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 D. Quillen, "The  cohomology of extraspecial 2groups and the spinor groups," Math. Ann., v. 194, 1971, pp. 197212. MR 0290401 (44:7582)
 [11]
 D. Rusin, The Cohomology of Groups Generated by Involutions, Thesis, Univ. of Chicago, 1984.
 [12]
 D. Rusin, "The  cohomology of metacyclic 2groups," J. Pure Appl. Algebra, v. 44, 1987, pp. 315327. 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)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198909681538
PII:
S 00255718(1989)09681538
Article copyright:
© Copyright 1989
American Mathematical Society
