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Depth-essential cohomology
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This page and its corresponding link will only appear if the
cohomology ring is not Cohen-Macaulay, that is, if the
Krull dimension of the cohomology ring does not equal its
depth.
In this page we define the depth-essential cohomology of the group,
we list centralizers of the elementary abelian subgroups whose ranks
exceed the depth of the cohomology ring by one, we provide generators
for the depth-essential cohomology, we give the dimension of its
annihilator, and we also provide some information about the space
generated by the images of the transfers from these centralizers.
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DEss(G) is the depth-essential cohomology of G, it is the intersection of kernels
of the restrictions to the centralizers of the elementary abelian p-subgroups
whose rank is one more than the depth of the cohomology ring of the group
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There is only one conjugacy class of subgroups which are centralizers of
elementary abelian subgroups of such a rank.
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The intersection of the images of transfers from these centralizers is denoted by
DI
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Centralizer C number
1
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Generators:
g2
g3
g4
,
g3
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DEss(G) is the ideal of P generated by:
z
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The annihilator of DEss(G) has dimension
1
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Let Q be the subring Q of P generated by:
w
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Then DEss(G) is a free module over Q generated by:
z
,
zy
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The ideal DI is the image of the transfer from the unique centralizer
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