Displaying 601 – 620 of 667

Showing per page

Cotorsion-free algebras as endomorphism algebras in L - the discrete and topological cases

Rüdiger E. Göbel, Brendan Goldsmith (1993)

Commentationes Mathematicae Universitatis Carolinae

The discrete algebras A over a commutative ring R which can be realized as the full endomorphism algebra of a torsion-free R -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, V = L . 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...

Countable extensions of torsion Abelian groups

Peter Vassilev Danchev (2005)

Archivum Mathematicum

Suppose A is an abelian torsion group with a subgroup G such that A / G is countable that is, in other words, A is a torsion countable abelian extension of G . A problem of some group-theoretic interest is that of whether G 𝕂 , a class of abelian groups, does imply that A 𝕂 . 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 𝕂 coincides with the class of all totally projective p -groups.

Counting arithmetic subgroups and subgroup growth of virtually free groups

Amichai Eisenmann (2015)

Journal of the European Mathematical Society

Let K be a p -adic field, and let H = P S L 2 ( K ) endowed with the Haar measure determined by giving a maximal compact subgroup measure 1 . Let A L H ( x ) denote the number of conjugacy classes of arithmetic lattices in H with co-volume bounded by x . We show that under the assumption that K does not contain the element ζ + ζ - 1 , where ζ denotes the p -th root of unity over p , we have lim x log A L H ( x ) x log x = q - 1 where q denotes the order of the residue field of K .

Counting fixed points of a finitely generated subgroup of Aff [C].

F. Loray, M. Van Der Put, F. Recher (2004)

Publicacions Matemàtiques

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.

Currently displaying 601 – 620 of 667