Journal of Algebra and Its Applications最新文献

{"title":"Finite p-groups in which the cores of all the nonnormal subgroups are in the center","authors":"Libo Zhao, Yangming Li, Lü Gong, Xiuyun Guo","doi":"10.1142/s0219498825502020","DOIUrl":"https://doi.org/10.1142/s0219498825502020","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> be a finite <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>p</mi></math></span><span></span>-group. Then <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> is said to be a <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi><mi>Z</mi></math></span><span></span>-group if <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>H</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>≤</mo><mi>Z</mi><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo></math></span><span></span> for every nonnormal subgroup <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>H</mi></math></span><span></span> of <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>. In this paper, we study the <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi><mi>Z</mi></math></span><span></span>-group <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> and get <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>c</mi><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo><mo>≤</mo><mn>3</mn></math></span><span></span>. It is proved that <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">exp</mtext></mstyle><mo stretchy=\"false\">(</mo><msup><mrow><mi>G</mi></mrow><mrow><mi>′</mi></mrow></msup><mo stretchy=\"false\">)</mo><mo>=</mo><mi>p</mi></math></span><span></span> if <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><mi>c</mi><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mn>2</mn></math></span><span></span> and <span><math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"><mo>|</mo><mi>G</mi><mo>|</mo><mo>≤</mo><msup><mrow><mi>p</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span><span></span> if <span><math altimg=\"eq-00016.gif\" display=\"inline\" overflow=\"scroll\"><mi>c</mi><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mn>3</mn></math></span><span></span>.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150765","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}

{"title":"Relative Gorenstein flat modules and Foxby classes and their model structures","authors":"Driss Bennis, Rachid El Maaouy, J. R. García Rozas, Luis Oyonarte","doi":"10.1142/s0219498825501944","DOIUrl":"https://doi.org/10.1142/s0219498825501944","url":null,"abstract":"<p>We introduce the concepts of relative (strongly) cotorsion and relative Gorenstein cotorsion modules for a non-necessarily semidualizing module and prove that there exists a unique hereditary abelian model structure where the cofibrations are the monomorphisms with relative Gorenstein flat cokernel and the fibrations are the epimorphisms with relative cotorsion kernel belonging to the Bass class. In the particular case of a semidualizing module, we investigate the existence of abelian model structures on the category of left (right) R-modules where the cofibrations are the epimorphisms (monomorphisms) with kernel (cokernel) belonging to the Bass (Auslander) class. We also show that the class of relative Gorenstein flat modules and the Bass class are part of weak AB-contexts.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153914","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}

{"title":"On the norm of the lower central series in a finite group","authors":"Lü Gong, Ziru Jing, Libo Zhao, Baojun Li","doi":"10.1142/s0219498825502032","DOIUrl":"https://doi.org/10.1142/s0219498825502032","url":null,"abstract":"<p>In this paper, the norm <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo></math></span><span></span> of the lower central series in a finite group <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> is introduced, which unifies the norm of derived subgroups and nilpotent residuals. Some propositions of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo></math></span><span></span> are obtained, and some related subgroups as well as their equivalent propositions can also be found.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153910","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}

{"title":"Quandles with one nontrivial column","authors":"Nicholas Cazet","doi":"10.1142/s0219498825502019","DOIUrl":"https://doi.org/10.1142/s0219498825502019","url":null,"abstract":"<p>The axioms of a quandle imply that the columns of its Cayley table are permutations. This paper studies quandles with exactly one non-trivially permuted column. Their automorphism groups, quandle polynomials, (symmetric) cohomology groups, and <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">Hom</mtext></mstyle></math></span><span></span> quandles are studied. The quiver and cocycle invariant of links using these quandles are shown to relate to linking number.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153920","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}

{"title":"On finite groups with weakly σ-normal subgroups","authors":"Juping Tang, Jiuzhou Ji, Nanying Yang","doi":"10.1142/s0219498825502172","DOIUrl":"https://doi.org/10.1142/s0219498825502172","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139961274","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}

{"title":"Left and right hybrid (b,c)-core inverses in semigroups with involution","authors":"Huihui Zhu, Chenxiang Hong, D. Mosić","doi":"10.1142/s0219498825502160","DOIUrl":"https://doi.org/10.1142/s0219498825502160","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139960441","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}

{"title":"On Computing Finite Index Subgroups of PSL2(ℤ)","authors":"Nicolas Mayorga Uruburu, Ariel Pacetti, Leandro Vendramin","doi":"10.1142/s0219498825502159","DOIUrl":"https://doi.org/10.1142/s0219498825502159","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139962597","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}

{"title":"Superpower Graphs of Finite Groups","authors":"Ajay Kumar, Lavanya Selvaganesh, Peter J. Cameron, T. Tamizh Chelvam","doi":"10.1142/s0219498825502147","DOIUrl":"https://doi.org/10.1142/s0219498825502147","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139963055","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}

{"title":"Investigation of ID-Derivations of Finite-Dimensional Nilpotent Lie Algebras","authors":"S. M. Moosavinejad, Farshid Saeedi","doi":"10.1142/s0219498825502135","DOIUrl":"https://doi.org/10.1142/s0219498825502135","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139963385","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}

{"title":"Cohomology and deformation theory of crossed homomorphisms of Leibniz algebras","authors":"Yizheng Li, Dingguo Wang","doi":"10.1142/s0219498825501956","DOIUrl":"https://doi.org/10.1142/s0219498825501956","url":null,"abstract":"<p>In this paper, we construct a differential graded Lie algebra whose Maurer–Cartan elements are given by crossed homomorphisms on Leibniz algebras. This allows us to define cohomology for a crossed homomorphism. Finally, we study linear deformations, formal deformations and extendibility of finite order deformations of a crossed homomorphism in terms of the cohomology theory.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150604","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}