Smooth invariants and -graded modules over
It is shown that every -graded module over is a direct sum of cyclics. The invariants for such modules are exactly the smooth invariants of valuated abelian -groups.
It is shown that every -graded module over is a direct sum of cyclics. The invariants for such modules are exactly the smooth invariants of valuated abelian -groups.
The remarkable development of the theory of smooth quasigroups is surveyed.
MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40The paper contains some new formulas involving the Whittaker functions and arising as the values of some double integrals, which are invariant with respect to the representation of the group SO(2; 1).
We shall show that there exist sofic groups which are not locally embeddable into finite Moufang loops. These groups serve as counterexamples to a problem and two conjectures formulated in the paper by M. Vodička, P. Zlatoš (2019).
We introduce and study the lattice of normal subgroups of a group G that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of G, see [Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883]. A precise description of this lattice is given for some particular classes of finite groups.
Si studiano i gruppi risolubili non di Černikov a quozienti propri di Černikov. Nel caso periodico tali gruppi sono tutti e soli i prodotti semidiretti con -gruppo abeliano elementare infinito e gruppo irriducibile di automorfismi di che sia infinito e di Černikov. Nel caso non periodico invece si riconduce tale studio a quello dei moduli a quozienti...