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Extension of Partial Automorphisms in Finite Tournament: Announcement 有限对局中部分自同构的推广：公告
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-02-12 DOI: 10.1007/s10469-026-09815-7
K. Zh. Kudaibergenov
{"title":"Extension of Partial Automorphisms in Finite Tournament: Announcement","authors":"K. Zh. Kudaibergenov","doi":"10.1007/s10469-026-09815-7","DOIUrl":"10.1007/s10469-026-09815-7","url":null,"abstract":"<p>We announce a positive solution to the partial automorphism extension problem for finite tournaments in the case of a unique partial automorphism, along with an estimate for the order of the resulting extension. We also announce the result that every finite tournament can be embedded into a finite vertex-transitive tournament, with the order of this vertex -transitive tournament specified. Complete proofs will be published in Algebra Logic <b>64</b>, No. 3 (2025).</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 2","pages":"92 - 95"},"PeriodicalIF":0.6,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338768","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
Reduction of the Group Isomorphism Problem to the Group Automorphism Problem 群同构问题约简为群自同构问题
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-02-11 DOI: 10.1007/s10469-026-09817-5
S. V. Skresanov
{"title":"Reduction of the Group Isomorphism Problem to the Group Automorphism Problem","authors":"S. V. Skresanov","doi":"10.1007/s10469-026-09817-5","DOIUrl":"10.1007/s10469-026-09817-5","url":null,"abstract":"<p>It is well known that the graph isomorphism problem is polynomial-time reducible to the graph automorphism problem (in fact, these two problems are polynomial-time equivalent). We show that the group isomorphism problem is polynomial-time reducible to the group automorphism problem. Reductions to other relevant problems like automorphism counting are also given.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 2","pages":"105 - 112"},"PeriodicalIF":0.6,"publicationDate":"2026-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338074","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
Triangular and Near-Trivial Quandles 三角形和近乎琐碎的纠缠
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-02-11 DOI: 10.1007/s10469-026-09813-9
A. N. Borodin, M. V. Neshchadim, A. A. Simonov
{"title":"Triangular and Near-Trivial Quandles","authors":"A. N. Borodin,&nbsp;M. V. Neshchadim,&nbsp;A. A. Simonov","doi":"10.1007/s10469-026-09813-9","DOIUrl":"10.1007/s10469-026-09813-9","url":null,"abstract":"<p>We define and study properties of triangular and near-trivial quandles.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 2","pages":"67 - 83"},"PeriodicalIF":0.6,"publicationDate":"2026-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336030","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
On Doubly Transitive Groups 关于双传递群
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-02-11 DOI: 10.1007/s10469-026-09816-6
M. V. Neshchadim, A. A. Simonov
{"title":"On Doubly Transitive Groups","authors":"M. V. Neshchadim,&nbsp;A. A. Simonov","doi":"10.1007/s10469-026-09816-6","DOIUrl":"10.1007/s10469-026-09816-6","url":null,"abstract":"<p>Using a 3-pseudofield, we construct doubly transitive groups that are restricted sharply 3-transitive groups for which the stabilizer of three points is trivial.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 2","pages":"96 - 104"},"PeriodicalIF":0.6,"publicationDate":"2026-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338073","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
On Locally Finite Groups with Bounded Number of Non-Locally-Solvable Factors 非局部可解因子有限个数的局部有限群
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-02-11 DOI: 10.1007/s10469-026-09814-8
A. A. Buturlakin
{"title":"On Locally Finite Groups with Bounded Number of Non-Locally-Solvable Factors","authors":"A. A. Buturlakin","doi":"10.1007/s10469-026-09814-8","DOIUrl":"10.1007/s10469-026-09814-8","url":null,"abstract":"<p>Given a group <i>G</i>, we refer to the maximum number of non-locally-solvable factors in any finite subnormal series of any subgroup of <i>G</i> as the <i>b</i>-dimension of <i>G</i>. We describe the structure of locally finite groups of finite <i>b</i>-dimension. This generalizes some known results on periodic linear groups and locally finite groups of finite <i>c</i>-dimension.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 2","pages":"84 - 91"},"PeriodicalIF":0.6,"publicationDate":"2026-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338420","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
On Generic Complexity of Diophantine Problem in Parametric Form 关于参数形式的丢番图问题的一般复杂性
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-02-05 DOI: 10.1007/s10469-026-09811-x
A. N. Rybalov
{"title":"On Generic Complexity of Diophantine Problem in Parametric Form","authors":"A. N. Rybalov","doi":"10.1007/s10469-026-09811-x","DOIUrl":"10.1007/s10469-026-09811-x","url":null,"abstract":"<p>From the negative solution to Hilbert’s tenth problem it follows that there exist polynomials p(<i>a</i>, <i>x</i><sub>1</sub>, . . . , <i>x</i><sub><i>n</i></sub>) with integer coefficients such that there is no algorithm that, for any natural number a determines whether the equation <i>p</i>(<i>a</i>, <i>x</i><sub>1</sub>, . . . , <i>x</i><sub><i>n</i></sub>) = 0 has a solution in integers. Professor V. A. Romankov posed to the author the question whether this Diophantine problem in parametric form is generically decidable. Generic algorithms decide problems on sets of almost all inputs, providing an indefinite answer for the remaining rare inputs. We prove that for some polynomials p this problem can be undecidable in the classical sense, but generically decidable, whereas for others it remains generically undecidable.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 1","pages":"47 - 54"},"PeriodicalIF":0.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337100","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
Stable Varieties of Non-Associative Algebras 非结合代数的稳定变种
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-02-03 DOI: 10.1007/s10469-026-09810-y
A. V. Popov
{"title":"Stable Varieties of Non-Associative Algebras","authors":"A. V. Popov","doi":"10.1007/s10469-026-09810-y","DOIUrl":"10.1007/s10469-026-09810-y","url":null,"abstract":"<p>We give a positive answer to the following question: is it possible to define a linear operator <i>π</i><sub><i>x</i></sub> acting on the space of nonassociative polynomials linear in <i>x</i> such that the actions of <i>π</i><sub><i>x</i></sub> defined above for the associative, Lie, and Jordan cases arise as the corresponding quotient representations of this nonassociative operator <i>π</i><sub><i>x</i></sub>?</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 1","pages":"33 - 46"},"PeriodicalIF":0.6,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336813","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
Lattice Definability of Finite Matrix Rings 有限矩阵环的格可定义性
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-01-31 DOI: 10.1007/s10469-026-09808-6
S. S. Korobkov
{"title":"Lattice Definability of Finite Matrix Rings","authors":"S. S. Korobkov","doi":"10.1007/s10469-026-09808-6","DOIUrl":"10.1007/s10469-026-09808-6","url":null,"abstract":"<p>The author continues to study lattice isomorphisms of finite matrix rings. In this paper, it is proved that if <i>R = M</i><sub><i>n</i></sub>(<i>K</i>)<i>, </i><i>n</i> ≥ 3<i>, </i><i>K</i> is a finite ring with identity, and <i>φ</i> is a lattice isomorphism of a ring <i>R</i> onto a ring <i>R</i><sup><i>φ</i></sup>, then the following statements hold: (1) <i>R</i><sup><i>φ</i></sup> ≅ <i>R</i> and (2) if the additive group of the ring <i>R</i> is primary, then the lattice isomorphism <i>φ</i> is induced by a ring isomorphism or anti-isomorphism of <i>R</i> onto <i>R</i><sup><i>φ</i></sup><i>.</i></p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 1","pages":"11 - 25"},"PeriodicalIF":0.6,"publicationDate":"2026-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342953","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
On Joinability by Horizontal Broken Lines on the Engel Group 关于Engel群上水平折线的可接合性
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-01-26 DOI: 10.1007/s10469-026-09807-7
A. V. Greshnov, M. V. Tryamkin
{"title":"On Joinability by Horizontal Broken Lines on the Engel Group","authors":"A. V. Greshnov,&nbsp;M. V. Tryamkin","doi":"10.1007/s10469-026-09807-7","DOIUrl":"10.1007/s10469-026-09807-7","url":null,"abstract":"<p>We prove that almost all points of the Engel group 𝔼<sub><i>α,β</i></sub> are joined with its neutral element by basis horizontal <i>k</i>-broken lines <span>({L}_{k}^{varepsilon },kle 4,)</span> the links of which are segments of integral lines of basis horizontal left-invariant vector fields <i>X, Y</i> of the Lie algebra of the group 𝔼<sub><i>α,β</i></sub>. Furthermore, there exist elements of the group 𝔼<sub><i>α,β</i></sub> that cannot be joined by basis horizontal <i>k</i>-broken lines <span>({L}_{k}^{varepsilon },kle 4)</span>.We prove that all points of the Engel group 𝔼<sub><i>α,β</i></sub> are joined with its neutral element by basis horizontal k-broken lines <span>({L}_{k}^{varepsilon },kle 6)</span><i>.</i></p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 1","pages":"1 - 10"},"PeriodicalIF":0.6,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342163","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 Involutions of Almost Simple Groups and Their Applications 概单群对合的生成集及其应用
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-01-24 DOI: 10.1007/s10469-026-09809-5
Ya. N. Nuzhin
{"title":"Generating Sets of Involutions of Almost Simple Groups and Their Applications","authors":"Ya. N. Nuzhin","doi":"10.1007/s10469-026-09809-5","DOIUrl":"10.1007/s10469-026-09809-5","url":null,"abstract":"<p>We present recent progress on problems by G. Malle, J. Saxl, T. Weigel, and the author concerning generating sets of involutions with properties of minimal cardinality for finite simple groups and formulate a number of new problems on this topic. We indicate necessary and sufficient conditions for a finite group generated by three involutions, two of which commute, to be a group of automorphisms of a regular 3-polytope.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 1","pages":"26 - 32"},"PeriodicalIF":0.6,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341672","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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