Abstract:Letpbe a prime number, letdbe an integer and letGbe ad-generated finitep-group of nilpotency class smaller thanp. Then the number of possible isomorphism types for the modpcohomology algebra{H^{*}(G;{\mathbb{F}}_{p})}is bounded in terms ofpandd.
Let p be a prime number and let c, d be natural numbers. Then, the number of possible isomorphism types for the mod p cohomology algebra of a d-generated finite p-group of nilpotency class c is bounded by a function depending only on p, c and d.
We prove that for any prime $p$ the finite $p$-groups of fixed coclass have only finitely many different mod-$p$ cohomology rings between them. This was conjectured by Carlson; we prove it by first proving a stronger version for groups of fixed rank.
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