Corrigendum to "Operators and products in the lattice of existence varieties of regular semigroups".
The discrete algebras over a commutative ring which can be realized as the full endomorphism algebra of a torsion-free -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...
Suppose is an abelian torsion group with a subgroup such that is countable that is, in other words, is a torsion countable abelian extension of . A problem of some group-theoretic interest is that of whether , a class of abelian groups, does imply that . The aim of the present paper is to settle the question for certain kinds of groups, thus extending a classical result due to Wallace (J. Algebra, 1981) proved when coincides with the class of all totally projective -groups.
Let be a -adic field, and let endowed with the Haar measure determined by giving a maximal compact subgroup measure . Let denote the number of conjugacy classes of arithmetic lattices in with co-volume bounded by . We show that under the assumption that does not contain the element , where denotes the -th root of unity over , we have where denotes the order of the residue field of .
Given a finitely generated subgroup G of the group of affine transformations acting on the complex line C, we are interested in the quotient Fix( G)/G. The purpose of this note is to establish when this quotient is finite and in this case its cardinality. We give an application to the qualitative study of polynomial planar vector fields at a neighborhood of a nilpotent singular point.