STRICT REGULARITY FOR $2$ -COCYCLES OF FINITE GROUPS.

Let $\alpha $ be a complex-valued $2$ -cocycle of a finite group $G.$ A new concept of strict $\alpha $ -regularity is introduced and its basic properties are investigated. To illustrate the potential use of this concept, a new proof is offered to show that the number of orbits of G under its action on the set of complex-valued irreducible $\alpha _N$ -characters of N equals the number of $\alpha $ -regular conjugacy classes of G contained in $N,$ where N is a normal subgroup of $G.$ [ABSTRACT FROM AUTHOR]