Cohomology of uniserial p-adic space groups with cyclic point group

Orbit isomorphic skeleton groups

“…Motivated by the skeleton groups of maximal class, see [3], we consider p-adic uniserial space groups with cyclic point groups. It follows from [9,Lemma 11] that every such space group is split and uniquely determined, up to isomorphism, by the size of its point group; thus, the following convention covers the general case of space groups with cyclic point groups.…”

A family of finitep‐groups satisfying Carlson's depth conjecture

“…In these two cases the mod‐ p cohomology rings have been calculated using computational tools (see [12]). Another argument supporting the conjecture is that for a fixed prime p and $$r\ge p-1$$, the groups $$G_r$$ have isomorphic mod‐ p cohomology groups; not as rings, but as $$\mathbb {F}_p$$‐modules (see [7]). This last isomorphism comes from a universal object described in the category of cochain complexes together with a quasi‐isomorphism that induces an isomorphism at the level of spectral sequences.…”