Complex group rings and group C$$^*$$-algebras of group extensions

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 $$^*$$ ∗ -algebra