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Full-Text Articles in Physical Sciences and Mathematics
An Explicit Construction Of Kleinian Groups With Small Limit Sets, Andrew Lazowski
An Explicit Construction Of Kleinian Groups With Small Limit Sets, Andrew Lazowski
Mathematics Faculty Publications
This paper provides an explicit construction of Kleinian groups that have small Hausdorff dimension of their limit sets. It is known that such groups exist and they can be constructed by results of Patterson. The purpose here is to work out the methods of calculation.
Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part I, Carol Jacoby, Katrin Leistner, Peter Loth, Lutz Strungmann
Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part I, Carol Jacoby, Katrin Leistner, Peter Loth, Lutz Strungmann
Mathematics Faculty Publications
We consider the class of abelian groups possessing partial decomposition bases in Lδ∞ω for δ an ordinal. This class contains the class of Warfield groups which are direct summands of simply presented groups or, alternatively, are abelian groups possessing a nice decomposition basis with simply presented cokernel. We prove a classification theorem using numerical invariants that are deduced from the classical Ulm-Kaplansky and Warfield invariants. This extends earlier work by Barwise-Eklof, Göbel and the authors.
Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part Ii, Carol Jacoby, Peter Loth
Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part Ii, Carol Jacoby, Peter Loth
Mathematics Faculty Publications
We consider abelian groups with partial decomposition bases in Lδ∞ω for ordinals δ. Jacoby, Leistner, Loth and Str¨ungmann developed a numerical invariant deduced from the classical global Warfield invariant and proved that if two groups have identical modified Warfield invariants and Ulm-Kaplansky invariants up to ωδ for some ordinal δ, then they are equivalent in Lδ∞ω. Here we prove that the modified Warfield invariant is expressible in Lδ∞ω and hence the converse is true for appropriate δ.
On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth
On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth
Mathematics Faculty Publications
A proper short exact sequence in the category of locally compact abelian groups is said to be t-pure if φ(A) is a topologically pure subgroup of B, that is, if for all positive integers n. We establish conditions under which t-pure exact sequences split and determine those locally compact abelian groups K ⊕ D (where K is compactly generated and D is discrete) which are t-pure injective or t-pure projective. Calling the extension (*) almost pure if for all positive integers n, we obtain a complete description of the almost pure injectives and almost pure projectives in the category of …
Pure Extensions Of Locally Compact Abelian Groups, Peter Loth
Pure Extensions Of Locally Compact Abelian Groups, Peter Loth
Mathematics Faculty Publications
In this paper, we study the group Pext(C,A) for locally compact abelian (LCA) groups A and C. Sufficient conditions are established for Pext(C,A) to coincide with the first Ulm subgroup of Ext(C,A). Some structural information on pure injectives in the category of LCA groups is obtained. Letting K denote the class of LCA groups which can be written as the topological direct sum of a compactly generated group and a discrete group, we determine the groups G in K which are pure injective in the category of LCA groups. Finally we describe those groups G in K such that every …
Compact Topologically Torsion Elements Of Topological Abelian Groups, Peter Loth
Compact Topologically Torsion Elements Of Topological Abelian Groups, Peter Loth
Mathematics Faculty Publications
In this note, we prove that in a Hausdorff topological abelian group, the closed subgroup generated by all compact elements is equal to teh closed subgroup generated by all compact elements which are topologically p-torsion for some prime p. In particular, this yields a new, short solution to a question raised by Armacost [A]. Using Pontrjagin duality, we obtain new descriptions of the identity component of a locally compact abelian group.
Normal Lattices And Coseparation Of Lattices, Barry B. Mittag
Normal Lattices And Coseparation Of Lattices, Barry B. Mittag
Mathematics Faculty Publications
No abstract provided.