Projective representations, abelian \(F\)-groups, and central extensions
Let \(F^*\) be the multiplicative group of a field \(F\), let \(G\) be a finite group and let \(\alpha \in Z^ 2(G,F^*)\). Denote by \(F^ \alpha G\) the corresponding twisted group algebra. The main result of the paper is the following Theorem: Finding a group \(G\) with a noncobounding 2- cocycle \(\alpha\) of finite order such that all \(F\)-classes of \(G\) are \(D_ \Gamma\)-regular for \(\Gamma= F^ \alpha G\) is equivalent to finding a group \(H\) with \(p'\)-cyclic subgroup \(A\) such that a primitive \(| A|\)-th root of unity is contained in \(F\), \(1 \neq A \subseteq Z(H) \cap H'(F)\), and such that \(A\) contains no \(F\)-commutator elements of \(H\) except the identity (here \(H'(F)\) is the group generated by all \(F\)-commutators in \(H\)).
scientific article; zbMATH DE number 436489