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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
Decidable Categoricity Spectra for Almost Prime Models 几乎质数模型的可判定分类谱系
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-07-30 DOI: 10.1007/s10469-024-09746-1
N. A. Bazhenov, M. I. Marchuk
{"title":"Decidable Categoricity Spectra for Almost Prime Models","authors":"N. A. Bazhenov,&nbsp;M. I. Marchuk","doi":"10.1007/s10469-024-09746-1","DOIUrl":"10.1007/s10469-024-09746-1","url":null,"abstract":"<p>We study decidable categoricity spectra for almost prime models. For any computable collection {D<sub>i</sub>}<sub>i∈ω</sub>, where D<sub>i</sub> either is a c.e. set or D<sub>i</sub> = PA, we construct a sequence of almost prime models {<span>({mathcal{M}}_{i})</span>}<sub>i∈ω</sub> elementarily embedded in each other, in which case for any i there exists a finite collection of constants such that the model <span>({mathcal{M}}_{i})</span> in the expansion by these constants has degree of decidable categoricity deg<sub>T</sub> (D<sub>i</sub>), if D<sub>i</sub> is a c.e. set, and has no degree of decidable categoricity if D<sub>i</sub> = PA. The result obtained extends that of S. S. Goncharov, V. Harizanov, and R. Miller [Sib. Adv. Math., 30, No. 3, 200-212 (2020)].</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 4","pages":"291 - 302"},"PeriodicalIF":0.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873323","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 : 2024-07-27 DOI: 10.1007/s10469-024-09752-3
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-024-09752-3","DOIUrl":"10.1007/s10469-024-09752-3","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 4","pages":"376 - 377"},"PeriodicalIF":0.4,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414270","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
Complexity of the Problem of ∀-Representation for Sentences 句子∀-表示问题的复杂性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-07-27 DOI: 10.1007/s10469-024-09751-4
N. T. Kogabaev
{"title":"Complexity of the Problem of ∀-Representation for Sentences","authors":"N. T. Kogabaev","doi":"10.1007/s10469-024-09751-4","DOIUrl":"10.1007/s10469-024-09751-4","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 4","pages":"372 - 375"},"PeriodicalIF":0.4,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141797562","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
Von Neumann Regular Hyperrings and Applications to Real Reduced Multirings 冯-诺依曼正则超环及其在实还原多重环中的应用
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-05-09 DOI: 10.1007/s10469-024-09739-0
H. R. O. Ribeiro, H. L. Mariano
{"title":"Von Neumann Regular Hyperrings and Applications to Real Reduced Multirings","authors":"H. R. O. Ribeiro,&nbsp;H. L. Mariano","doi":"10.1007/s10469-024-09739-0","DOIUrl":"10.1007/s10469-024-09739-0","url":null,"abstract":"<p>A multiring is a ring-like structure where the sum is multivalued and a hyperring is a multiring with a strong distributive property. With every multiring we associate a structural presheaf, and when that presheaf is a sheaf, we say that the multiring is geometric. A characterization of geometric von Neumann hyperrings is presented. And we build a von Neumann regular hull for multirings which is used in applications to algebraic theory of quadratic forms. Namely, we describe the functor Q, introduced by M. Marshall in [J. Pure Appl. Alg., <b>205</b>, No. 2, 452-468 (2006)], as a left adjoint functor for the natural inclusion of the category of real reduced multirings (similar to real semigroups) into the category of preordered multirings and explore some of its properties. Next, we employ sheaf-theoretic methods to characterize real reduced hyperrings as certain geometric von Neumann regular real hyperrings and construct the functor V , a geometric von Neumann regular hull for a multiring. Finally, we look at some interesting logical and algebraic interactions between the functors Q and V that are useful for describing hyperrings in the image of the functor Q and that will allow us to explore the theory of quadratic forms for (formally) real semigroups.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 3","pages":"215 - 256"},"PeriodicalIF":0.4,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140933959","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
Order Positive Fields. I 订购积极领域。I
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-04-22 DOI: 10.1007/s10469-024-09738-1
M. V. Korovina, O. V. Kudinov
{"title":"Order Positive Fields. I","authors":"M. V. Korovina,&nbsp;O. V. Kudinov","doi":"10.1007/s10469-024-09738-1","DOIUrl":"10.1007/s10469-024-09738-1","url":null,"abstract":"<p>The notion of a computable structure based on numberings with decidable equality is well established with a number of prominent results. Nevertheless, applied to strictly ordered fields, it fails to capture some natural properties and constructions for which decidability of equality is not assumed. For example, the field of primitive recursive real numbers is not computable, and there exists a computable real closed field with noncomputable maximal Archimedean subfields. We introduce the notion of an order positive field which aims to overcome these limitations. A general criterion is presented which decides when an Archimedean field is order positive. Using this criterion, we show that the field of primitive recursive real numbers is order positive and that the Archimedean parts of order positive real closed fields are order positive. We also state a program for further research.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 3","pages":"203 - 214"},"PeriodicalIF":0.4,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140675957","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
Pretabularity and Craig’s Interpolation Property 预圆周率和克雷格插值特性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-04-19 DOI: 10.1007/s10469-024-09742-5
L. L. Maksimova, V. F. Yun
{"title":"Pretabularity and Craig’s Interpolation Property","authors":"L. L. Maksimova,&nbsp;V. F. Yun","doi":"10.1007/s10469-024-09742-5","DOIUrl":"10.1007/s10469-024-09742-5","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 3","pages":"277 - 282"},"PeriodicalIF":0.4,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140682811","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 : 2024-04-19 DOI: 10.1007/s10469-024-09745-2
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-024-09745-2","DOIUrl":"10.1007/s10469-024-09745-2","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 3","pages":"289 - 290"},"PeriodicalIF":0.4,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412377","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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