Abstract Let N and H be groups, let G an extension of by . In this article, we describe the structure complex group ring in terms data associated with particular, present conditions on building blocks guaranteeing that satisfies zero-divisor idempotent conjectures. Moreover, for central extensions involving amenable groups Kadison–Kaplansky conjecture holds C $$^*$$ <mml:math xmlns:mml="http://...

Introduction. Let G be a group, K an invariant subgroup of G. The purpose of this paper is to investigate the relations between the cohomology groups of G, K, and G/K. As in the case of fibre spaces, it turns out that such relations can be expressed by a spectral sequence whose term E2 is HiG/K, HiK)) and whose term Em is the graduated group associated with i7(G). This problem was first studied...