Central units in p-adic group rings (Q1099230)

Let p be a prime, let G be a finite p-group, and let R denote the ring of integers in some finite unramified extension of the field of p-adic numbers. The author constructs a natural exact sequence of groups \[ 1 \to <(-1)^{p-1}>\times Z(G) \to 1+JZRG \to ZRG \to <(-1)^{p-1}>\times Z(G) \to 1. \] If A is a finite group acting on G then A acts also on \(M:=(1+JZRG)/(<(-1)^{p-1}>\times Z(G))\). Using the exact sequence above, the author shows that \(H^ 1(A,M)=0\), thus answering a question raised by the reviewer.