Cohomology of groups with metacyclic Sylow $p$-subgroups
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- by Jill Dietz, John Martino and Stewart Priddy PDF
- Proc. Amer. Math. Soc. 124 (1996), 2261-2266 Request permission
Abstract:
We determine the cohomology algebras $H^{*}(G;\mathbf {F}_{p})$ for all groups $G$ with a metacyclic Sylow $p$-subgroup. The complete $p$-local stable decomposition of the classifying space $BG$ is also determined.References
- D. J. Benson and M. Feshbach, Stable splittings of classifying spaces of finite groups, Topology 31 (1992), no. 1, 157–176. MR 1153243, DOI 10.1016/0040-9383(92)90068-S
- Thomas Diethelm, The $\textrm {mod}\,p$ cohomology rings of the nonabelian split metacyclic $p$-groups, Arch. Math. (Basel) 44 (1985), no. 1, 29–38. MR 778989, DOI 10.1007/BF01193778
- Jill Dietz, Stable splittings of classifying spaces of metacyclic $p$-groups, $p$ odd, J. Pure Appl. Algebra 90 (1993), no. 2, 115–136. MR 1250764, DOI 10.1016/0022-4049(93)90125-D
- Jill Dietz, Stable splittings of classifying spaces of metacyclic $2$-groups, Math. Proc. Cambridge Philos. Soc. 116 (1994), no. 2, 285–299. MR 1281547, DOI 10.1017/S0305004100072583
- D. J. Glover, A study of certain modular representations, J. Algebra 51 (1978), no. 2, 425–475. MR 476841, DOI 10.1016/0021-8693(78)90116-3
- John C. Harris and Nicholas J. Kuhn, Stable decompositions of classifying spaces of finite abelian $p$-groups, Math. Proc. Cambridge Philos. Soc. 103 (1988), no. 3, 427–449. MR 932667, DOI 10.1017/S0305004100065038
- Johannes Huebschmann, The mod-$p$ cohomology rings of metacyclic groups, J. Pure Appl. Algebra 60 (1989), no. 1, 53–103. MR 1014607, DOI 10.1016/0022-4049(89)90107-2
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703, DOI 10.1007/978-3-642-64981-3
- John R. Martino, Classifying spaces of $p$-groups with cyclic maximal subgroups, Topology and representation theory (Evanston, IL, 1992) Contemp. Math., vol. 158, Amer. Math. Soc., Providence, RI, 1994, pp. 157–174. MR 1263716, DOI 10.1090/conm/158/01457
- J. Martino and S. Priddy, On the cohomology and homotopy of Swan groups (to appear).
- John Martino and Stewart Priddy, The complete stable splitting for the classifying space of a finite group, Topology 31 (1992), no. 1, 143–156. MR 1153242, DOI 10.1016/0040-9383(92)90067-R
- John Martino and Stewart Priddy, Classification of $BG$ for groups with dihedral or quarternion Sylow $2$-subgroups, J. Pure Appl. Algebra 73 (1991), no. 1, 13–21. MR 1121628, DOI 10.1016/0022-4049(91)90103-9
Additional Information
- Jill Dietz
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- Address at time of publication: Department of Mathematics and Computer Science, Gettysburg College, Gettysburg, Pennsylvania 17325
- Email: jdietz@gettysburg.edu
- John Martino
- Affiliation: Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, Michigan 49008
- Email: martino@wmich.edu
- Stewart Priddy
- Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
- Email: s_priddy@math.nwu.edu
- Received by editor(s): January 26, 1995
- Additional Notes: The third author is partially supported by NSF Grant DMS-9400235.
- Communicated by: Thomas Goodwillie
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2261-2266
- MSC (1991): Primary 55R35; Secondary 20J06
- DOI: https://doi.org/10.1090/S0002-9939-96-03389-8
- MathSciNet review: 1328344