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Locally Finite Groups Containing Direct Products of Dihedral Groups 含二面体群的直积的局部有限群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-14 DOI: 10.1007/s10469-025-09785-2
A. A. Shlepkin
{"title":"Locally Finite Groups Containing Direct Products of Dihedral Groups","authors":"A. A. Shlepkin","doi":"10.1007/s10469-025-09785-2","DOIUrl":"10.1007/s10469-025-09785-2","url":null,"abstract":"<p>We prove the theorem stating the following. Let <i>G</i> be a locally finite group saturated with groups from a set 𝔐 consisting of direct products of <i>d</i> dihedral groups. Then <i>G</i> is a direct product of d groups of the form <i>B</i> ⋋ &lt;υ&gt;, where <i>B</i> is a locally cyclic group inverted by an involution υ.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"217 - 227"},"PeriodicalIF":0.4,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091051","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
Decidable Models of Ehrenfeucht Theories 埃伦费希理论的可决定模型
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-05 DOI: 10.1007/s10469-025-09779-0
P. E. Alaev, E. I. Khlestova
{"title":"Decidable Models of Ehrenfeucht Theories","authors":"P. E. Alaev,&nbsp;E. I. Khlestova","doi":"10.1007/s10469-025-09779-0","DOIUrl":"10.1007/s10469-025-09779-0","url":null,"abstract":"<p>We study countable models of Ehrenfeucht theories, i.e., complete theories with a finite number of countable models, strictly larger than 1. The notion of a primely generated model is introduced. It is proved that if all complete types of an Ehrenfeucht theory have arithmetic complexity, then any of the primely generated models of the theory possesses an arithmetically complex isomorphic presentation.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"155 - 163"},"PeriodicalIF":0.4,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091032","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
Wielandt 𝔛 -Subgroups Wielandt𝔛-子组
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-03 DOI: 10.1007/s10469-025-09784-3
D. O. Revin
{"title":"Wielandt 𝔛 -Subgroups","authors":"D. O. Revin","doi":"10.1007/s10469-025-09784-3","DOIUrl":"10.1007/s10469-025-09784-3","url":null,"abstract":"<p>Let 𝔛 be a nonempty class of finite groups closed under taking subgroups, homomorphic images, and extensions. We define the concept of a Wielandt 𝔛 -subgroup in an arbitrary finite group. It generalizes the concept of a submaximal 𝔛 -subgroup introduced by H. Wielandt and is key in the framework of a program proposed by Wielandt in 1979. One of the central objectives of the program is to overcome difficulties associated with the reduction to factors of a subnormal series within the natural problem of searching for maximal 𝔛 -subgroups. Wielandt 𝔛 -subgroups possess a number of properties unshareable by submaximal 𝔛 -subgroups. There is a hope that, due to these additional properties, the use of Wielandt 𝔛 -subgroups will open up new possibilities in realizing Wielandt’s program.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"201 - 216"},"PeriodicalIF":0.4,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091018","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
CEA-Operators and the Ershov Hierarchy. I cea -算子和Ershov层次。我
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-02 DOI: 10.1007/s10469-025-09780-7
M. M. Arslanov, I. I. Batyrshin, M. M. Yamaleev
{"title":"CEA-Operators and the Ershov Hierarchy. I","authors":"M. M. Arslanov,&nbsp;I. I. Batyrshin,&nbsp;M. M. Yamaleev","doi":"10.1007/s10469-025-09780-7","DOIUrl":"10.1007/s10469-025-09780-7","url":null,"abstract":"<p>We consider the relationship between the CEA-hierarchy and the Ershov hierarchy in <span>({Delta }_{2}^{0})</span> Turing degrees. A degree <b>c</b> is called CEA(<b>a</b>) if <b>c</b> is computably enumerable in <b>a</b>, and <b>a</b> ≤ <b>c</b>. Soare and Stob [Stud. Logic Found. Math., <b>107</b>, 299-324 (1982)] proved that for a noncomputable low c.e. degree <b>a</b> there exists a CEA(<b>a</b>) degree that is not c.e. Later, Arslanov, Lempp, and Shore [Ann. Pure Appl. Logic, <b>78</b>, Nos. 1-3, 29-56 (1996)] formulated the problem of describing pairs of degrees <b>a</b> &lt; <b>e</b> such that there exists a CEA(<b>a</b>) 2-c.e. degree <b>d</b> ≤ <b>e</b> which is not c.e. Since then the question has remained open as to whether a CEA(<b>a</b>) degree in the sense of Soare and Stob can be made 2-c.e. Here we answer this question in the negative, solving it in a stronger formulation: there exists a noncomputable low c.e. degree <b>a</b> such that any CEA(<b>a</b>) ω-c.e. degree is c.e. Also possible generalizations of the result obtained are discussed, as well as various issues associated with the problem mentioned.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"164 - 178"},"PeriodicalIF":0.4,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091015","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
Connected Pseudofinite Unars 连通的伪有限元
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-01 DOI: 10.1007/s10469-025-09782-5
E. L. Efremov, A. A. Stepanova, S. G. Chekanov
{"title":"Connected Pseudofinite Unars","authors":"E. L. Efremov,&nbsp;A. A. Stepanova,&nbsp;S. G. Chekanov","doi":"10.1007/s10469-025-09782-5","DOIUrl":"10.1007/s10469-025-09782-5","url":null,"abstract":"<p>We start studying the structure of pseudofinite unars. Necessary (sufficient) conditions of being pseudofinite are formulated for connected unars without cycles, containing no chains, and we give examples showing that these conditions are not sufficient (resp. necessary). It is noted that a coproduct of chains is a pseudofinite unar; in particular, a chain is a pseudofinite unar. A nonpseudofinite unar without cycles, containing exactly one chain is exemplified. For connected unars without cycles, containing two chains, we formulate a necessary condition of being pseudofinite and give an example of a nonpseudofinite unar.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"186 - 194"},"PeriodicalIF":0.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090989","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
Punctual Spectra of Algebraic Structures and Isomorphisms 代数结构和同构的准时谱
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-04-30 DOI: 10.1007/s10469-025-09786-1
N. A. Bazhenov, I. Sh. Kalimullin
{"title":"Punctual Spectra of Algebraic Structures and Isomorphisms","authors":"N. A. Bazhenov,&nbsp;I. Sh. Kalimullin","doi":"10.1007/s10469-025-09786-1","DOIUrl":"10.1007/s10469-025-09786-1","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"228 - 231"},"PeriodicalIF":0.4,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091193","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
Absolute Indiscernibility 绝对不可辨认性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-04-29 DOI: 10.1007/s10469-025-09783-4
K. Zh. Kudaibergenov
{"title":"Absolute Indiscernibility","authors":"K. Zh. Kudaibergenov","doi":"10.1007/s10469-025-09783-4","DOIUrl":"10.1007/s10469-025-09783-4","url":null,"abstract":"<p>We look into the question about conditions under which any permutation of an indiscernible subset of a model extends to an automorphism of the model.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"195 - 200"},"PeriodicalIF":0.4,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091074","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
Isomorphism of Atomless Boolean Algebras with Distinguished Ideals 具有杰出理想的无原子布尔代数的同构
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-04-29 DOI: 10.1007/s10469-025-09781-6
S. S. Goncharov, J. Xiang
{"title":"Isomorphism of Atomless Boolean Algebras with Distinguished Ideals","authors":"S. S. Goncharov,&nbsp;J. Xiang","doi":"10.1007/s10469-025-09781-6","DOIUrl":"10.1007/s10469-025-09781-6","url":null,"abstract":"<p>An algebraic, model-theoretic, and algorithmic theory of enriched Boolean algebras with distinguished ideals was developed in a series of papers by D. E. Pal’chunov, A. Touraille, P. E. Alaev, N. T. Kogabaev, and other authors. Here we study the problem on the number of countable Boolean algebras with distinguished ideals for the case when an algebra and its quotient with respect to a distinguished ideal are atomless. It is proved that, for this subclass, there exist continuum many such countable structures.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"179 - 185"},"PeriodicalIF":0.4,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091163","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 : 2025-04-29 DOI: 10.1007/s10469-025-09787-0
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-025-09787-0","DOIUrl":"10.1007/s10469-025-09787-0","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"232 - 234"},"PeriodicalIF":0.4,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091164","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
Duality for Bi-Algebraic Lattices Belonging to the Variety of (0, 1)-Lattices Generated by the Pentagon 属于五边形生成的(0,1)-格的双代数格的对偶性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-01-31 DOI: 10.1007/s10469-025-09776-3
W. Dziobiak, M. V. Schwidefsky
{"title":"Duality for Bi-Algebraic Lattices Belonging to the Variety of (0, 1)-Lattices Generated by the Pentagon","authors":"W. Dziobiak,&nbsp;M. V. Schwidefsky","doi":"10.1007/s10469-025-09776-3","DOIUrl":"10.1007/s10469-025-09776-3","url":null,"abstract":"<p>According to G. Birkhoff, there is a categorical duality between the category of bi-algebraic distributive (0, 1)-lattices with complete (0, 1)-lattice homomorphisms as morphisms and the category of partially ordered sets with partial order-preserving maps as morphisms. We extend this classical result to the bi-algebraic lattices belonging to the variety of (0, 1)-lattices generated by the pentagon, the 5-element nonmodular lattice. Applying the extended duality, we prove that the lattice of quasivarieties contained in the variety of (0, 1)-lattices generated by the pentagon has uncountably many elements and is not distributive. This yields the following: the lattice of quasivarieties contained in a nontrivial variety of (0, 1)-lattices either is a 2-element chain or has uncountably many elements and is not distributive.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 2","pages":"114 - 140"},"PeriodicalIF":0.4,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109883","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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