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- W1529478544 abstract "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 $mathcal {O}$ 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 $mathcal {O}$. Assume also that $mathcal {O}$ is closed under conjugation and that $E$ is in $mathcal {O}$ whenever some subgroup of $E$ is in $mathcal {O}$. Then there exists a regular element $zeta$ in the cohomology ring $H^*(BG,k)$ such that the restriction of $zeta$ to an elementary abelian $p$-subgroup $E$ is not nilpotent if and only if $E$ is in $mathcal {O}$. 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." @default.
- W1529478544 created "2016-06-24" @default.
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- W1529478544 date "1996-01-01" @default.
- W1529478544 modified "2023-09-25" @default.
- W1529478544 title "Cohomological detection and regular elements in group cohomology" @default.
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- W1529478544 doi "https://doi.org/10.1090/s0002-9939-96-03331-x" @default.
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