A group $G$ is said to be $\frac{3}{2}$-generated if every nontrivial element belongs a generating pair. It easy see that has this property, then proper quotient of cyclic. In paper we prove the converse true for finite groups, which settles conjecture Breuer, Guralnick and Kantor from 2008. fact, much stronger result, solves problem posed by Brenner Wiegold in 1975. Namely, cyclic, any pair el...

Given a variety with finite group action, we compare its equivariant categorical measure, that is, the measure of corresponding quotient stack, and extended quotient. Using weak factorization for orbifolds, show wide range cases these two measures coincide. This implies, in particular, conjecture Galkin Shinder on motivic zeta-functions varieties. We provide examples showing that, general, are ...