A note on the projective representations of finite groups (Q1962577)

The author considers projective complex representations of a finite group \(G\) with a given cocycle \(\alpha\). The main result of the paper reads as follows. Let \(P_1,\dots,P_n\) be the Sylow \(p_i\)-subgroups of \(G\), where \(p_1,\dots,p_n\) are the primes dividing the order of \(G\). If \(M_i\) is a subgroup of \(P_i\) of minimal order such that the cohomology class of the restriction of \(\alpha\) to \(M_i\) is trivial, then the greatest common divisor of the degrees of the projective characters of \(G\) with cocycle \(\alpha\) equals \(\prod_{i=1}^n[P_i:M_i]\). Several corollaries are also given.