Cohomological detection and regular elements in group cohomology
Cohomological detection and regular elements in group cohomology
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群上同调中的上同调检测和正则元素
DOI：
10.1090/s0002-9939-96-03331-x
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
H. Henn
中科院分区：
文献类型：
--
作者：
J. Carlson;H. Henn
.设G是紧李群或有限虚上同调维数的离散群，k是特征p > 0的域.设O是初等交换p -子群G的集合，使得上同调H（cid：3）（BG;k）在O的元素的中心化子上可检测.还假设O在共轭下是闭的，并且只要E的某个子群在O中，E就在O中。则在上同调环H（cid：3）（BG;k）中存在正则元（cid：16）使得（cid：16）对初等交换p -子群E的限制不是幂零的当且仅当E在O中.该结果的匡威是Lannes、Schwartz和第二作者的一个定理。这些结果对上同调环的深度和相关的素数有几个影响。
. Suppose that G is a compact Lie group or a discrete group of (cid:12)nite virtual cohomological dimension and that k is a (cid:12)eld of characteristic p > 0. Suppose that O is a set of elementary abelian p -subgroups G such that the cohomology H (cid:3) ( 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 (cid:16) in the cohomology ring H (cid:3) ( BG;k ) such that the restriction of (cid:16) 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.