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Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$-adic spacegroup of dimension $d_x=(p-1)p^{x-1}$ and with cyclic point group of order$p^x$. In this short note we prove that all the quotients of $R$ of size biggerthan or equal to $p^{d_x+x}$ have isomorphic mod $p$ cohomology groups. Inparticular, we show that the cohomology groups of sufficiently large quotientsof the unique maximal class pro-$p$ group are isomorphic as $\F_p$-modules.

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