Cohomological detection and regular elements in group cohomology
Suppose that G is a compact Lie group or a discrete group of finite virtual cohomological dimension and that k is a field of characteristic p > 0. Suppose that O is a set of elementary abelian p-subgroups G such that the cohomology H∗(BG, k) is detected on the centralizers of the elements of O. Ass...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
1996
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| In: |
Proceedings of the American Mathematical Society
Year: 1996, Jahrgang: 124, Heft: 3, Pages: 665-670 |
| ISSN: | 1088-6826 |
| DOI: | 10.1090/S0002-9939-96-03331-X |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1090/S0002-9939-96-03331-X Verlag, lizenzpflichtig, Volltext: http://www.ams.org/proc/1996-124-03/S0002-9939-96-03331-X/ 
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| Verfasserangaben: | Jon F. Carlson, Hans-Werner Henn |
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| 520 | |a Suppose that G is a compact Lie group or a discrete group of finite virtual cohomological dimension and that k is a field of characteristic p > 0. Suppose that O is a set of elementary abelian p-subgroups G such that the cohomology H∗(BG, k) is detected on the centralizers of the elements of O. Assume also that O is closed under conjugation and that E is in O whenever some subgroup of E is in O. Then there exists a regular element ζ in the cohomology ring H∗(BG, k) such that the restriction of ζ to an elementary abelian p-subgroup E is not nilpotent if and only if E is in O. The converse of the result is a theorem of Lannes, Schwartz and the second author. The results have several implications for the depth and associated primes of the cohomology rings. | ||
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