Schur's theorem and its generalisation, Baer's theorem, are distinguished results in group theory, connecting the upper central quotients with lower series. The aim of this paper is to generalise these two different directions, using novel methods related non-abelian tensor product. In particular, we prove a version Schur–Baer for finitely generated groups. Then, apply newly obtained describe k...

‎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.

Recently, the authors obtained Schur multiplier, non-abelian tensor square and exterior of $d$-generator generalized Heisenberg Lie algebras rank $ \frac{1}{2}d(d-1).$ Here, we intend to obtain same results for t$ when \frac{1}{2}d(d-1)-3 \leq t\leq \frac{1}{2}d(d-1)-1.$ Then, as a result, give similar consequences nilpotent algebra L class two \dim (L/Z(L))=d,$ L^2=t such that

Consider analytical three-dimensional differential systems having a singular point at the origin such that its linear part is y∂x−λz∂z for some λ≠0. The restriction of to Center Manifold has nilpotent origin. We prove if restricted system analytic and center origin, with Andreev number 2, then admits formal inverse Jacobi multiplier. also centers systems, on manifolds, are limits Hopf-type cent...

Given a nilpotent Lie algebra L of dimension $$\le 6$$ on an arbitrary field characteristic $$\ne 2$$ , we show direct method to detect whether is capable or not via computations the size its nonabelian exterior square $$L \wedge L$$ . For dimensions higher than 6, result general nature, based evidences low dimensional case, but also large families algebras, namely generalized Heisenberg algebr...