The Bogomolov multiplier is a group theoretical invariant isomorphic to the unramified Brauer group of a given quotient space. We derive a homological version of the Bogomolov multiplier, prove a Hopf-type formula, find a five term exact sequence corresponding to this invariant, and describe the role of the Bogomolov multiplier in the theory of central extensions. A new description of the Bogom...

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

Let p be a prime number. We give the explicit structure of 2-nilpotent multiplier for each finite 2-generator p-group class two. Moreover, 2-capable groups in that are characterized.