LAUSR

Abstract Let p be a fixed prime number and let R denote a uniserial p -adic space group of dimension d x = p x − 1 ( p − 1 ) and with cyclic point group of order p x . In this short note we prove that all the quotients of R of size bigger than or equal to p d x + x have isomorphic mod p cohomology groups. In particular, we show that the cohomology groups of sufficiently large quotients of the unique maximal class pro- p group are isomorphic as F p -modules.