International Journal of Algebra and Computation最新文献

{"title":"A branch group in a class of non-contracting weakly regular branch groups","authors":"Sagar Saha, K. V. Krishna","doi":"10.1142/s021819672450036x","DOIUrl":"https://doi.org/10.1142/s021819672450036x","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141675772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the dimensions of the graded space 𝔽2 ⊗𝒜𝔽2[x1,x2,…,xs] at degrees s + 5 and its relation to algebraic transfers","authors":"Dang Vo Phuc","doi":"10.1142/s0218196724500401","DOIUrl":"https://doi.org/10.1142/s0218196724500401","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141674211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the representation of fields as sums of two proper subfields","authors":"M. Kepczyk","doi":"10.1142/s0218196724500395","DOIUrl":"https://doi.org/10.1142/s0218196724500395","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141675256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Clonoids between modules","authors":"Peter Mayr, Patrick Wynne","doi":"10.1142/s021819672450022x","DOIUrl":"https://doi.org/10.1142/s021819672450022x","url":null,"abstract":"<p>Clonoids are sets of finitary functions from an algebra <span><math altimg=\"eq-00001.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A</mtext></mstyle></math></span><span></span> to an algebra <span><math altimg=\"eq-00002.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">B</mtext></mstyle></math></span><span></span> that are closed under composition with term functions of <span><math altimg=\"eq-00003.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A</mtext></mstyle></math></span><span></span> on the domain side and with term functions of <span><math altimg=\"eq-00004.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">B</mtext></mstyle></math></span><span></span> on the codomain side. For <span><math altimg=\"eq-00005.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A, B</mtext></mstyle></math></span><span></span> (polynomially equivalent to) finite modules we show: If <span><math altimg=\"eq-00006.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A, B</mtext></mstyle></math></span><span></span> have coprime order and the congruence lattice of <span><math altimg=\"eq-00007.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A</mtext></mstyle></math></span><span></span> is distributive, then there are only finitely many clonoids from <span><math altimg=\"eq-00008.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A</mtext></mstyle></math></span><span></span> to <span><math altimg=\"eq-00009.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">B</mtext></mstyle></math></span><span></span>. This is proved by establishing for every natural number <span><math altimg=\"eq-00010.gif\" display=\"inline\"><mi>k</mi></math></span><span></span> a particular linear equation that all <span><math altimg=\"eq-00011.gif\" display=\"inline\"><mi>k</mi></math></span><span></span>-ary functions from <span><math altimg=\"eq-00012.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A</mtext></mstyle></math></span><span></span> to <span><math altimg=\"eq-00013.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">B</mtext></mstyle></math></span><span></span> satisfy. Else if <span><math altimg=\"eq-00014.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A, B</mtext></mstyle></math></span><span></span> do not have coprime order, then there exist infinite ascending chains of clonoids from <span><math altimg=\"eq-00015.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A</mtext></mstyle></math></span><span></span> to <span><math altimg=\"eq-00016.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">B</mtext></mstyle></math></span><span></span> ordered by inclusion. Consequently any extension of <span><math altimg=\"eq-00017.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">A</mtext></mstyle></math></span><span></span> by <span><math altimg=\"eq-00018.gif\" display=\"inline\"><mstyle><mtext mathvariant=\"normal\">B</mtext></mstyle></math></span><span></span> has countably infinitely many <","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141198021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"There are no post-quantum weakly pseudo-free families in any nontrivial variety of expanded groups","authors":"Mikhail Anokhin","doi":"10.1142/s0218196724500188","DOIUrl":"https://doi.org/10.1142/s0218196724500188","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\"><mi mathvariant=\"normal\">Ω</mi></math></span><span></span> be a finite set of finitary operation symbols and let <span><math altimg=\"eq-00002.gif\" display=\"inline\"><mi>𝔙</mi></math></span><span></span> be a nontrivial variety of <span><math altimg=\"eq-00003.gif\" display=\"inline\"><mi mathvariant=\"normal\">Ω</mi></math></span><span></span>-algebras. Assume that for some set <span><math altimg=\"eq-00004.gif\" display=\"inline\"><mi mathvariant=\"normal\">Γ</mi><mo>⊆</mo><mi mathvariant=\"normal\">Ω</mi></math></span><span></span> of group operation symbols, all <span><math altimg=\"eq-00005.gif\" display=\"inline\"><mi mathvariant=\"normal\">Ω</mi></math></span><span></span>-algebras in <span><math altimg=\"eq-00006.gif\" display=\"inline\"><mi>𝔙</mi></math></span><span></span> are groups under the operations associated with the symbols in <span><math altimg=\"eq-00007.gif\" display=\"inline\"><mi mathvariant=\"normal\">Γ</mi></math></span><span></span>. In other words, <span><math altimg=\"eq-00008.gif\" display=\"inline\"><mi>𝔙</mi></math></span><span></span> is assumed to be a nontrivial variety of expanded groups. In particular, <span><math altimg=\"eq-00009.gif\" display=\"inline\"><mi>𝔙</mi></math></span><span></span> can be a nontrivial variety of groups or rings. Our main result is that there are no post-quantum weakly pseudo-free families in <span><math altimg=\"eq-00010.gif\" display=\"inline\"><mi>𝔙</mi></math></span><span></span>, even in the worst-case setting and/or the black-box model. In this paper, we restrict ourselves to families <span><math altimg=\"eq-00011.gif\" display=\"inline\"><mo stretchy=\"false\">(</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>d</mi></mrow></msub><mi>|d</mi><mo>∈</mo><mi>D</mi><mo stretchy=\"false\">)</mo></math></span><span></span> of computational and black-box <span><math altimg=\"eq-00012.gif\" display=\"inline\"><mi mathvariant=\"normal\">Ω</mi></math></span><span></span>-algebras (where <span><math altimg=\"eq-00013.gif\" display=\"inline\"><mi>D</mi><mo>⊆</mo><msup><mrow><mo stretchy=\"false\">{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">}</mo></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup></math></span><span></span>) such that for every <span><math altimg=\"eq-00014.gif\" display=\"inline\"><mi>d</mi><mo>∈</mo><mi>D</mi></math></span><span></span>, each element of <span><math altimg=\"eq-00015.gif\" display=\"inline\"><msub><mrow><mi>H</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span><span></span> is represented by a unique bit string of length polynomial in the length of <span><math altimg=\"eq-00016.gif\" display=\"inline\"><mi>d</mi></math></span><span></span>. In our main result, we use straight-line programs to represent nontrivial relations between elements of <span><math altimg=\"eq-00017.gif\" display=\"inline\"><mi mathvariant=\"normal\">Ω</mi></math></span><span></span>-algebras. Note that under certain conditions, this result depends on the classification of finite simple gr","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the lattice of closed subgroups of a profinite group","authors":"Francesco de Giovanni, Iker de las Heras, Marco Trombetti","doi":"10.1142/s0218196724500206","DOIUrl":"https://doi.org/10.1142/s0218196724500206","url":null,"abstract":"<p>The subgroup lattice of a group is a great source of information about the structure of the group itself. The aim of this paper is to use a similar tool for studying profinite groups. In more detail, we study the lattices of closed or open subgroups of a profinite group and its relation with the whole group. We show, for example, that procyclic groups are the only profinite groups with a distributive lattice of closed or open subgroups, and we give a sharp characterization of profinite groups whose lattice of closed (or open) subgroups satisfies the Dedekind modular law; we actually give a precise description of the behavior of modular elements of the lattice of closed subgroups. We also deal with the problem of carrying some structural information from a profinite group to another one having an isomorphic lattice of closed (or open) subgroups. Some interesting consequences and related results concerning decomposability and the number of profinite groups with a given lattice of closed (or open) subgroups are also obtained.</p>","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An algorithm to recognize echelon subgroups of a free group","authors":"Dario Ascari","doi":"10.1142/s021819672450019x","DOIUrl":"https://doi.org/10.1142/s021819672450019x","url":null,"abstract":"<p>We provide an algorithm that, given a finite set of generators for a subgroup <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>H</mi></math></span><span></span> of a finitely generated free group <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>F</mi></math></span><span></span>, determines whether <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>H</mi></math></span><span></span> is echelon or not and, in case of affirmative answer, also computes a basis with respect to which <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>H</mi></math></span><span></span> is in echelon form. This gives an answer to a question of Rosenmann. We also prove, by means of a counterexample, that intersection of two echelon subgroups needs not to be echelon, answering another question of Rosenmann.</p>","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140841938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Properties of congruence lattices of graph inverse semigroups","authors":"Marina Anagnostopoulou-Merkouri, Zachary Mesyan, James D. Mitchell","doi":"10.1142/s0218196724500139","DOIUrl":"https://doi.org/10.1142/s0218196724500139","url":null,"abstract":"<p>From any directed graph <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span> one can construct the graph inverse semigroup <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, whose elements, roughly speaking, correspond to paths in <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span>. Wang and Luo showed that the congruence lattice <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo></math></span><span></span> of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is upper-semimodular for every graph <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span>, but can fail to be lower-semimodular for some <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span>. We provide a simple characterization of the graphs <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span> for which <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo></math></span><span></span> is lower-semimodular. We also describe those <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span> such that <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo></math></span><span></span> is atomistic, and characterize the minimal generating sets for <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo></math></span><span></span> when <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span> is finite and simple.</p>","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dependence over subgroups of free groups","authors":"A. Rosenmann, Enric Ventura","doi":"10.1142/s0218196724500176","DOIUrl":"https://doi.org/10.1142/s0218196724500176","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140737860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"p-Singular characters and normal sylow p-subgroups","authors":"Weijun Liu, Qinghong Guo, Lihua Feng, Zheng Huang","doi":"10.1142/s0218196724500164","DOIUrl":"https://doi.org/10.1142/s0218196724500164","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140740957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}