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Diameter and Laplace Eigenvalue Estimates for Left-invariant Metrics on Compact Lie Groups
Let G be a compact connected Lie group of dimension m . Once a bi-invariant metric on G is fixed, left-invariant metrics on G are in correspondence...
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Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups
In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4,...
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c-compactness in locally compact groups and paratopological groups
We study c -compactness in two cases. First, we obtain some subclasses of locally compact groups where compactness and c -compactness coincide, and...
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Left-invariant geometries on SU(2) are uniformly doubling
A classical aspect of Riemannian geometry is the study of estimates that hold uniformly over some class of metrics. The best known examples are...
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Maximal subgroups and strong completeness of profinite groups
It is proved that all subgroups of finite index in a profinite group G are open if and only if G has only countably many abstract maximal subgroups...
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On Linear Configurations in Subsets of Compact Abelian Groups, and Invariant Measurable Hypergraphs
We prove an arithmetic removal result for all compact abelian groups, generalizing a finitary removal result of Král’, Serra, and the third author....
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A local stability principle for continuous group homomorphisms in nonstandard setting
We state a simple fact relating some continuity and homomorphy properties of an internal map** between nonstandard extensions of topological groups...
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Coverings and dimensions in infinite profinite groups
Answering a question of Miklós Abért, we prove that an infinite profinite group cannot be the union of less than continuum many translates of a...
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Idempotents and the multiplicative group of some totally bounded rings
In this paper, we extend some results of D.Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a...
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A note on just-non-Ω groups
Extending some previous notions in literature, we consider the class of just-non-Ω groups, where Ω is a prevariety of topological groups. Some...
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Pattern closure of groups of tree automorphisms
It is shown that every group of automorphisms of a regular rooted tree that is defined by forbidding a set of patterns of size s + 1 is the...
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A decomposition theorem for compact groups with an application to supercompactness
We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor...
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Compact domination for groups definable in linear o-minimal structures
We prove the Compact Domination Conjecture for groups definable in linear o-minimal structures. Namely, we show that every definably compact group G ...
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Valdivia compact Abelian groups
Let
R denote the smallest class of compact spaces containing all metric compacta and closed under limits of continuous inverse sequences of... -
G-compactness and groups
Lascar described E KP as a composition of E L and the topological closure of E L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this...
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A duality property of an uncountable product of \({\mathbb{Z}}\)
We construct a quotient group of an uncountable product of integers which is not Pontryagin reflexive.
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Factorization of Cosine Functions on Compact Connected Groups
Based on the structure theorem of compact connected groups, the following factorization theorem is obtained in this paper: if a compact connected...
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Weyl Transforms, Heat Kernels, Green Functions and Riemann Zeta Functions on Compact Lie Groups
The Plancherel formula and the inversion formula for Weyl transforms on compact and Hausdorff groups are given. A formula expressing the...