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- W2021487779 abstract "Let k[G] be the group algebra of a polycyclic-by-finite group G over a field k. We show that, for any finitely generated k[G]-module V, H∗(G,V)=⊕n≥0Hn(G,V) is a Noetherian module over the cohomology algebra H∗(G,k). In particular, the power series PG(V; t)=Σn≥0dimkHn(G, V)tnϵZ〚t〛 is a rational function in t of the form f(t)/Πi=1s (1−tki), where f(t)ϵZ[t]. For example, if G has no non-trivial finite normal subgroups and contains a torsion-free normal subgroup of index 2 and char k=2, then we show that PG(V; −1) is always defined and equals (−1)hρ(V)/ρ(k[G]), where h=h(G) is the Hirsch number of G and ρ(·) denotes the Goldie rank." @default.
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- W2021487779 date "1986-01-01" @default.
- W2021487779 modified "2023-10-16" @default.
- W2021487779 title "On the cohomology of polycyclic-by-finite groups" @default.
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- W2021487779 doi "https://doi.org/10.1016/0022-4049(86)90031-9" @default.
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