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Box-Quasimetrics and Horizontal Joinability on Cartan Groups Cartan群上的盒拟测度和水平接合性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-21 DOI: 10.1007/s10469-024-09767-w
A. V. Greshnov, V. S. Kostyrkin
{"title":"Box-Quasimetrics and Horizontal Joinability on Cartan Groups","authors":"A. V. Greshnov,&nbsp;V. S. Kostyrkin","doi":"10.1007/s10469-024-09767-w","DOIUrl":"10.1007/s10469-024-09767-w","url":null,"abstract":"<p>On a Cartan group <span>({mathbb{K}})</span> equipped with a Carnot–Carathéodory metric <i>d</i><sub><i>cc</i></sub>, we find the exact value of a constant in the (1, <i>q</i><sub>2</sub>)-generalized triangle inequality for its Box-quasimetric. It is proved that any two points <i>x</i>, <i>y</i> ∈ <span>({mathbb{K}})</span> can be joined by a horizontal <i>k</i>-broken line <span>({L}_{x,y}^{k})</span>, <i>k</i> ≤ 6; moreover, the length of such a broken line <span>({L}_{x,y}^{k})</span> does not exceed the quantity <i>Cd</i><sub><i>cc</i></sub>(<i>x</i>, <i>y</i>) for some constant <i>C</i> not depending on the choice of <i>x</i>, <i>y</i> ∈ <span>({mathbb{K}})</span>. The value 6 here is nearly optimal.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 1","pages":"10 - 20"},"PeriodicalIF":0.4,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Residual π-Finiteness of Tubular Groups 管群的残差π有限性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-21 DOI: 10.1007/s10469-024-09768-9
F. A. Dudkin, A. V. Usikov
{"title":"Residual π-Finiteness of Tubular Groups","authors":"F. A. Dudkin,&nbsp;A. V. Usikov","doi":"10.1007/s10469-024-09768-9","DOIUrl":"10.1007/s10469-024-09768-9","url":null,"abstract":"<p>A finitely generated group<i> G</i>, which acts on a tree so that all edge stabilizers are infinite cyclic groups and all vertex stabilizers are free rank 2 Abelian groups, is called a tubular group. Every tubular group is isomorphic to the fundamental group <i>π</i><sub>1</sub>(𝒢) of a suitable finite graph 𝒢 of groups. We prove a criterion for residual <i>π</i>-finiteness of tubular groups presented by trees of groups. Also we state a criterion for residual p-finiteness of tubular groups whose corresponding graph contains one edge outside a maximal subtree.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 1","pages":"28 - 41"},"PeriodicalIF":0.4,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Levi Classes of Quasivarieties of Nilpotent Groups of Class at Most Two 最多两个类的幂零群的拟变异的李维类
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-19 DOI: 10.1007/s10469-024-09761-2
S. A. Shakhova
{"title":"Levi Classes of Quasivarieties of Nilpotent Groups of Class at Most Two","authors":"S. A. Shakhova","doi":"10.1007/s10469-024-09761-2","DOIUrl":"10.1007/s10469-024-09761-2","url":null,"abstract":"<p>A Levi class <span>(Lleft(mathcal{M}right))</span> generated by a class <span>(left(mathcal{M}right))</span> of groups is the class of all groups in which the normal closure of every cyclic subgroup belongs to <span>(left(mathcal{M}right))</span>. Let p be a prime and <i>p</i> ≠ 2, let <i>H</i><sub><i>p</i></sub> be a free group of rank 2 in the variety of nilpotent groups of class at most 2 with commutator subgroup of exponent <i>p</i>, and let <i>qH</i><sub><i>p</i></sub> be the quasivariety generated by the group <i>H</i><sub><i>p</i></sub>. It is shown that there exists a set of quasivarieties <span>(mathcal{M})</span> of cardinality continuum such that <span>(Lleft(mathcal{M}right))</span> = <i>L</i>(<i>qH</i><sub><i>p</i></sub>). Let <i>s</i> be a natural number, <i>s</i> ≥ 2. We specify a system of quasi-identities defining <i>L</i>(<i>q</i>(<i>H</i><sub><i>p</i></sub>, <span>({Z}_{{p}^{s}})</span>)), and prove that there exists a set of quasivarieties <span>(mathcal{M})</span> of cardinality continuum such that <span>(Lleft(mathcal{M}right))</span> = <i>L</i>(<i>q</i>(<i>H</i><sub><i>p</i></sub>, <span>({Z}_{{p}^{s}})</span>)), where <span>({Z}_{{p}^{s}})</span> is a cyclic group of order <i>p</i><sup><i>s</i></sup>; <i>q</i>(<i>H</i><sub><i>p</i></sub>, <span>({Z}_{{p}^{s}})</span>) is the quasivariety generated by the groups <i>H</i><sub><i>p</i></sub> and <span>({Z}_{{p}^{s}}.)</span></p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 6","pages":"501 - 515"},"PeriodicalIF":0.4,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Length of an Unsatisfiable Subformula 不可满足子公式的长度
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-19 DOI: 10.1007/s10469-024-09771-0
A. V. Seliverstov
{"title":"The Length of an Unsatisfiable Subformula","authors":"A. V. Seliverstov","doi":"10.1007/s10469-024-09771-0","DOIUrl":"10.1007/s10469-024-09771-0","url":null,"abstract":"<p>We find a bound for the length of a conjunction of some propositional formulas, for which every unsatisfiable formula contains an unsatisfiable subformula. In particular, this technique applies to formulas in conjunctive normal form with restrictions on the number of true literals within every elementary disjunction, as well as for 2-CNFs, for symmetric 3-CNFs, and for conjunctions of voting functions in three literals. A lower bound on the rank of some matrices is used in proofs.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 1","pages":"65 - 72"},"PeriodicalIF":0.4,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Isomorphisms between Incidence Algebras and Group Algebras 关联代数与群代数之间的若干同构
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-17 DOI: 10.1007/s10469-024-09766-x
I. V. Dudin, P. A. Krylov
{"title":"Some Isomorphisms between Incidence Algebras and Group Algebras","authors":"I. V. Dudin,&nbsp;P. A. Krylov","doi":"10.1007/s10469-024-09766-x","DOIUrl":"10.1007/s10469-024-09766-x","url":null,"abstract":"<p>Relations between some constructions based on incidence rings and group rings are considered.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 1","pages":"21 - 27"},"PeriodicalIF":0.4,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of Independent Quasi-Equational Bases. II 独立拟方程基的存在性。2
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-17 DOI: 10.1007/s10469-024-09762-1
M. V. Schwidefsky
{"title":"Existence of Independent Quasi-Equational Bases. II","authors":"M. V. Schwidefsky","doi":"10.1007/s10469-024-09762-1","DOIUrl":"10.1007/s10469-024-09762-1","url":null,"abstract":"<p>If a certain condition holds for a quasivariety <b>K</b> then <b>K</b> contains continuum many subquasivarieties having a finitely partitionable ω-independent quasi-equational basis relative to <b>K</b>. This is true, in particular, for each almost ff-universal quasivariety <b>K</b>.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 6","pages":"516 - 531"},"PeriodicalIF":0.4,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite Generatedness of Veronese Subalgebras of a Free Alternative Algebra of Finite Rank 有限秩自由替代代数的Veronese子代数的有限生成性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-17 DOI: 10.1007/s10469-024-09770-1
S. V. Pchelintsev, I. P. Shestakov
{"title":"Finite Generatedness of Veronese Subalgebras of a Free Alternative Algebra of Finite Rank","authors":"S. V. Pchelintsev,&nbsp;I. P. Shestakov","doi":"10.1007/s10469-024-09770-1","DOIUrl":"10.1007/s10469-024-09770-1","url":null,"abstract":"<p>It is proved that, for any natural <i>n</i>, the subalgebra generated by words of length divisible by <i>n</i> on generators (the Veronese <i>n</i>-subalgebra) in a free finitely generated alternative algebra is finitely generated.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 1","pages":"56 - 64"},"PeriodicalIF":0.4,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sessions of the Seminar “Algebra i Logika” “代数与逻辑学”研讨会分会场
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-16 DOI: 10.1007/s10469-024-09764-z
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-024-09764-z","DOIUrl":"10.1007/s10469-024-09764-z","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 6","pages":"548 - 551"},"PeriodicalIF":0.4,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Groups with Restrictions on Normal Subgroups 对正常子组有限制的组
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-16 DOI: 10.1007/s10469-024-09765-y
A. I. Budkin
{"title":"Groups with Restrictions on Normal Subgroups","authors":"A. I. Budkin","doi":"10.1007/s10469-024-09765-y","DOIUrl":"10.1007/s10469-024-09765-y","url":null,"abstract":"<p>It is proved that if <i>G</i> is a group without elements of order 2, and the normal closure of every 2-generated subgroup of <i>G</i> is a nilpotent group of class at most 3, then <i>G</i> will be a nilpotent group of class at most 4. It is also shown that the restriction on second-order elements cannot be lifted.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 1","pages":"1 - 9"},"PeriodicalIF":0.4,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sessions of the Seminar “Algebra i Logika” “代数与逻辑学”研讨会分会场
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-14 DOI: 10.1007/s10469-024-09772-z
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-024-09772-z","DOIUrl":"10.1007/s10469-024-09772-z","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 1","pages":"73 - 74"},"PeriodicalIF":0.4,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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