Box-Quasimetrics and Horizontal Joinability on Cartan Groups

IF 0.4 3区数学 Q4 LOGIC Algebra and Logic Pub Date : 2024-12-21 DOI:10.1007/s10469-024-09767-w

A. V. Greshnov, V. S. Kostyrkin

引用次数: 0

Abstract

On a Cartan group \({\mathbb{K}}\) equipped with a Carnot–Carathéodory metric d_cc, we find the exact value of a constant in the (1, q₂)-generalized triangle inequality for its Box-quasimetric. It is proved that any two points x, y ∈ \({\mathbb{K}}\) can be joined by a horizontal k-broken line \({L}_{x,y}^{k}\), k ≤ 6; moreover, the length of such a broken line \({L}_{x,y}^{k}\) does not exceed the quantity Cd_cc(x, y) for some constant C not depending on the choice of x, y ∈ \({\mathbb{K}}\). The value 6 here is nearly optimal.

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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.

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