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Wreath Products of Semigroups and Plotkin’s Problem 半群的花环积与普洛特金问题
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-10-04 DOI: 10.1007/s10469-024-09757-y
A. N. Shevlyakov
{"title":"Wreath Products of Semigroups and Plotkin’s Problem","authors":"A. N. Shevlyakov","doi":"10.1007/s10469-024-09757-y","DOIUrl":"10.1007/s10469-024-09757-y","url":null,"abstract":"<p>We prove that the wreath product <i>C</i> = <i>A</i> ≀ <i>B</i> of a semigroup A with zero and an infinite cyclic semigroup B is <b>q</b><sub><i>ω</i></sub>-compact (logically Noetherian). Our result partially solves I. Plotkin‘s problem for wreath products.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 5","pages":"448 - 467"},"PeriodicalIF":0.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409889","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
Generating Triples of Conjugate Involutions for Finite Simple Groups 有限简单群共轭旋转的三重生成
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-10-02 DOI: 10.1007/s10469-024-09753-2
M. A. Vsemirnov, Ya. N. Nuzhin
{"title":"Generating Triples of Conjugate Involutions for Finite Simple Groups","authors":"M. A. Vsemirnov,&nbsp;Ya. N. Nuzhin","doi":"10.1007/s10469-024-09753-2","DOIUrl":"10.1007/s10469-024-09753-2","url":null,"abstract":"<p>It is proved that among finite simple non-Abelian groups only the groups <i>U</i><sub>3</sub>(3) and <i>A</i><sub>8</sub> are not generated by three conjugate involutions. This result is obtained modulo a known conjecture on the description of finite simple groups generated by two elements of orders 2 and 3.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 5","pages":"379 - 397"},"PeriodicalIF":0.4,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409491","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
Stone Dualities for Distributive Posets 分配式 Posets 的石头二重性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-09-30 DOI: 10.1007/s10469-024-09756-z
M. V. Schwidefsky
{"title":"Stone Dualities for Distributive Posets","authors":"M. V. Schwidefsky","doi":"10.1007/s10469-024-09756-z","DOIUrl":"10.1007/s10469-024-09756-z","url":null,"abstract":"<p>A topological duality result is established for the category of distributive c-posets defined in this paper, as well as for some of its important full subcategories. All duality results presented extend the well-known topological duality result obtained by M. H. Stone for the category of distributive (0, 1)-lattices.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 5","pages":"430 - 447"},"PeriodicalIF":0.4,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415138","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
A Functorial Generalization of the Fitting Subgroup in Finite Groups 有限群中拟合子群的赋形泛化
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-09-27 DOI: 10.1007/s10469-024-09754-1
V. I. Murashko, A. F. Vasil’ev
{"title":"A Functorial Generalization of the Fitting Subgroup in Finite Groups","authors":"V. I. Murashko,&nbsp;A. F. Vasil’ev","doi":"10.1007/s10469-024-09754-1","DOIUrl":"10.1007/s10469-024-09754-1","url":null,"abstract":"<p>Using the functional approach of R. Baer and B. I. Plotkin, we introduce and study the notion of ℱ-functorial whose values are characteristic subgroups of a finite group that possess certain properties of the Fitting subgroup. The lattice and semigroups of ℱ-functorials are described, the interrelation between ℱ-functorials and classes of groups is established, a characterization of their values is given in terms of group’s elements inducing inner automorphisms on specified chief factors.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 5","pages":"398 - 412"},"PeriodicalIF":0.4,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414527","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
Associative and Jordan Lie Nilpotent Algebras 联立和乔丹烈无穷级数
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-09-19 DOI: 10.1007/s10469-024-09755-0
S. V. Pchelintsev
{"title":"Associative and Jordan Lie Nilpotent Algebras","authors":"S. V. Pchelintsev","doi":"10.1007/s10469-024-09755-0","DOIUrl":"10.1007/s10469-024-09755-0","url":null,"abstract":"<p>We look at the interconnection between Lie nilpotent Jordan algebras and Lie nilpotent associative algebras. It is proved that a special Jordan algebra is Lie nilpotent if and only if its associative enveloping algebra is Lie nilpotent. Also it turns out that a Jordan algebra is Lie nilpotent of index 2n + 1 if and only if its algebra of multiplications is Lie nilpotent of index 2n. Finally, we prove a product theorem for Jordan algebras.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 5","pages":"413 - 429"},"PeriodicalIF":0.4,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268616","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 "研讨会课程
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-09-13 DOI: 10.1007/s10469-024-09758-x
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-024-09758-x","DOIUrl":"10.1007/s10469-024-09758-x","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 5","pages":"468 - 470"},"PeriodicalIF":0.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411614","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
Projections of Finite Rings 有限环的投影
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-08-16 DOI: 10.1007/s10469-024-09750-5
S. S. Korobkov
{"title":"Projections of Finite Rings","authors":"S. S. Korobkov","doi":"10.1007/s10469-024-09750-5","DOIUrl":"10.1007/s10469-024-09750-5","url":null,"abstract":"<p>Let <i>R</i> and <i>R</i><sup><i>φ</i></sup> be associative rings with isomorphic subring lattices, and <i>φ</i> be a lattice isomorphism (or else a projection) of the ring <i>R</i> onto the ring <i>R</i><sup><i>φ</i></sup>. We call <i>R</i><sup><i>φ</i></sup> the projective image of a ring <i>R</i> and call <i>R</i> itself the projective preimage of a ring <i>R</i><sup><i>φ</i></sup>. The main result of the first part of the paper is Theorem 5, which proves that the projective image <i>R</i><sup><i>φ</i></sup> of a one-generated finite <i>p</i>-ring <i>R</i> is also one-generated if <i>R</i><sup><i>φ</i></sup> at the same time is itself a <i>p</i>-ring. In the second part, we continue studying projections of matrix rings. The main result of this part is Theorems 6 and 7, which prove that if <i>R</i> = <i>M</i><sub><i>n</i></sub>(<i>K</i>) is the ring of all square matrices of order n over a finite ring K with identity, and <i>φ</i> is a projection of the ring <i>R</i> onto the ring <i>R</i><sup><i>φ</i></sup>, then <i>R</i><sup><i>φ</i></sup> = <i>M</i><sub><i>n</i></sub>(<i>K′</i>), where <i>K′</i> is a ring with identity, lattice-isomorphic to the ring <i>K</i>.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 4","pages":"353 - 371"},"PeriodicalIF":0.4,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190636","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
Generating Sets of Conjugate Involutions of Groups PSLn(9) PSLn(9) 群共轭旋转的生成集
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-08-14 DOI: 10.1007/s10469-024-09748-z
R. I. Gvozdev
{"title":"Generating Sets of Conjugate Involutions of Groups PSLn(9)","authors":"R. I. Gvozdev","doi":"10.1007/s10469-024-09748-z","DOIUrl":"10.1007/s10469-024-09748-z","url":null,"abstract":"<p>G. Malle, J. Saxl, and T. Weigel in [Geom. Ded., <b>49</b>, No. 1, 85-116 (1994)] formulated the following problem: For every finite simple non-Abelian group <i>G</i>, find the minimum number <i>n</i><sub><i>c</i></sub>(<i>G</i>) of generators of conjugate involutions whose product equals 1. (See also Question 14.69c in [Unsolved Problems in Group Theory. The Kourovka Notebook, No. 20, E. I. Khukhro and V. D. Mazurov (Eds.), Sobolev Institute of Mathematics SO RAN, Novosibirsk (2022); https://alglog.org/20tkt.pdf].) J. M. Ward [PhD Thesis, Queen Mary College, Univ. London (2009)] solved this problem for sporadic, alternating, and projective special linear groups <i>PSL</i><sub><i>n</i></sub>(<i>q</i>) over a field of odd order <i>q</i>, except in the case <i>q</i> = 9 for <i>n</i> ≥ 4 and also in the case <i>q</i> ≡ 3 (mod 4) for <i>n</i> = 6. Here we lift the restriction <i>q</i> ≠ 9 for dimensions <i>n</i> ≥ 9 and <i>n</i> = 6.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 4","pages":"319 - 338"},"PeriodicalIF":0.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190621","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
Modularity of the Lattice of Baer n-Multiply σ-Local Formations Baer n乘σ局部网格的模块性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-08-13 DOI: 10.1007/s10469-024-09747-0
N. N. Vorob’ev
{"title":"Modularity of the Lattice of Baer n-Multiply σ-Local Formations","authors":"N. N. Vorob’ev","doi":"10.1007/s10469-024-09747-0","DOIUrl":"10.1007/s10469-024-09747-0","url":null,"abstract":"<p>Let σ be a partition of the set of all prime numbers into a union of pairwise disjoint subsets. Using the idea of multiple localization due to A. N. Skiba, we introduce the notion of a Baer n-multiply σ-local formation of finite groups. It is proved that with respect to inclusion ⊆, the collection of all such formations form a complete algebraic modular lattice. Thereby we generalize the result obtained by A. N. Skiba and L. A. Shemetkov in [Ukr. Math. J., 52, No. 6, 783-797 (2000)].</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 4","pages":"303 - 318"},"PeriodicalIF":0.4,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190620","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
3-Generated Lattices Close to Distributive Ones 接近分配式网格的 3 代网格
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-08-05 DOI: 10.1007/s10469-024-09749-y
A. G. Gein, I. D. Maslintsyn, K. E. Maslintsyna, K. V. Selivanov
{"title":"3-Generated Lattices Close to Distributive Ones","authors":"A. G. Gein,&nbsp;I. D. Maslintsyn,&nbsp;K. E. Maslintsyna,&nbsp;K. V. Selivanov","doi":"10.1007/s10469-024-09749-y","DOIUrl":"10.1007/s10469-024-09749-y","url":null,"abstract":"<p>Lattices are considered in which, instead of distributive identities, a ‘gap’ of length at most 1 is allowed between the right and left parts of each distributivity relation. Such lattices are said to be close to distributive ones. Although this property is weaker than distributivity, nevertheless a 3-generated lattice with this property is also finite.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 4","pages":"339 - 352"},"PeriodicalIF":0.4,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947953","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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