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On some upper bounds on the intersection number of a finite soluble group 有限可溶群交点数的上界
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-23 DOI: 10.1007/s00013-025-02155-5
A. Ballester-Bolinches, R. V. Borodich, S. F. Kamornikov
{"title":"On some upper bounds on the intersection number of a finite soluble group","authors":"A. Ballester-Bolinches,&nbsp;R. V. Borodich,&nbsp;S. F. Kamornikov","doi":"10.1007/s00013-025-02155-5","DOIUrl":"10.1007/s00013-025-02155-5","url":null,"abstract":"<div><p>For a finite group <i>G</i>,  the <i>intersection number</i> <span>(alpha (G))</span> of <i>G</i> is the minimal number of maximal subgroups of <i>G</i> whose intersection coincides with <span>(Phi (G),)</span> the Frattini subgroup of <i>G</i>. In this paper, new upper bounds on <span>(alpha (G))</span> are established when <i>G</i> is soluble.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 3","pages":"227 - 234"},"PeriodicalIF":0.5,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02155-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maps preserving the maximal numerical range of the triple product of operators 保留算子的三重积的最大数值范围的映射
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-21 DOI: 10.1007/s00013-025-02148-4
Abdellatif Bourhim, Mohamed Mabrouk
{"title":"Maps preserving the maximal numerical range of the triple product of operators","authors":"Abdellatif Bourhim,&nbsp;Mohamed Mabrouk","doi":"10.1007/s00013-025-02148-4","DOIUrl":"10.1007/s00013-025-02148-4","url":null,"abstract":"<div><p>Let <span>(mathscr {L}(mathscr {H}))</span> be the algebra of all bounded linear operators on a complex Hilbert space <span>(mathscr {H})</span>. For an operator <span>(Tin mathscr {L}(mathscr {H}))</span>, let <span>(W_0(T))</span> be the maximal numerical range of <i>T</i>. We show that a map <span>(varphi )</span> from <span>(mathscr {L}(mathscr {H}))</span> onto itself satisfies </p><div><div><span>$$begin{aligned} W_0left( varphi (S)varphi (T)varphi (S)right) ~=~W_0(STS), qquad (T,~Sin mathscr {L}(mathscr {H})), end{aligned}$$</span></div></div><p>if and only if there are a unitary operator <span>(Uin mathscr {L}(mathscr {H}))</span> and <span>(lambda in mathbb {C})</span> such that <span>(lambda ^3=1)</span> and either <span>(varphi (T)= lambda UTU^*)</span> for all <span>(Tin mathscr {L}(mathscr {H}))</span>, or <span>(varphi (T)= lambda UT^top U^*)</span> for all <span>(Tin mathscr {L}(mathscr {H}))</span>. Here, <span>(T^top )</span> denotes the transpose of any operator <span>(Tin mathscr {L}(mathscr {H}))</span> relative to a fixed but arbitrary orthonormal base of <span>(mathscr {H})</span>. When the triple product “<i>STS</i>” is replaced by the skew-triple product “<span>(TS^*T)</span>”, we arrive at the same conclusion but with <span>(lambda =1)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 3","pages":"311 - 321"},"PeriodicalIF":0.5,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the Wakamatsu tilting conjecture 关于若松倾斜猜想
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-18 DOI: 10.1007/s00013-025-02147-5
Kamran Divaani-Aazar, Ali Mahin Fallah, Massoud Tousi
{"title":"On the Wakamatsu tilting conjecture","authors":"Kamran Divaani-Aazar,&nbsp;Ali Mahin Fallah,&nbsp;Massoud Tousi","doi":"10.1007/s00013-025-02147-5","DOIUrl":"10.1007/s00013-025-02147-5","url":null,"abstract":"<div><p>Let <i>R</i> be an associative ring with identity. We establish that the generalized Auslander–Reiten conjecture implies the Wakamatsu tilting conjecture. Furthermore, we prove that any Wakamatsu tilting <i>R</i>-module of finite projective dimension that is tensorly faithful is projective. By utilizing this result, we show the validity of the Wakamatsu tilting conjecture for <i>R</i> in two cases: when <i>R</i> is a left Artinian local ring or when it is the group ring of a finite group <i>G</i> over a commutative Artinian ring.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 3","pages":"291 - 302"},"PeriodicalIF":0.5,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Classification of non-F-split del Pezzo surfaces of degree 1 1次非f -分裂del Pezzo曲面的分类
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-16 DOI: 10.1007/s00013-025-02143-9
Gebhard Martin, Réka Wagener
{"title":"Classification of non-F-split del Pezzo surfaces of degree 1","authors":"Gebhard Martin,&nbsp;Réka Wagener","doi":"10.1007/s00013-025-02143-9","DOIUrl":"10.1007/s00013-025-02143-9","url":null,"abstract":"<div><p>Using Fedder’s criterion, we classify all non-<i>F</i>-split del Pezzo surfaces of degree 1. We give a necessary and sufficient criterion for the <i>F</i>-splitting of such del Pezzo surfaces in terms of their anti-canonical system.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 3","pages":"283 - 290"},"PeriodicalIF":0.5,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02143-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dirichlet dynamical zeta function for billiard flow 台球流的Dirichlet动态zeta函数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-16 DOI: 10.1007/s00013-025-02141-x
Vesselin Petkov
{"title":"Dirichlet dynamical zeta function for billiard flow","authors":"Vesselin Petkov","doi":"10.1007/s00013-025-02141-x","DOIUrl":"10.1007/s00013-025-02141-x","url":null,"abstract":"<div><p>We study the Dirichlet dynamical zeta function <span>(eta _D(s))</span> for billiard flow corresponding to several strictly convex disjoint obstacles. For large <span>({{,textrm{Re},}}s)</span>, we have <span>(eta _D(s) =sum _{n= 1}^{infty } a_n e^{-lambda _n s}, , a_n in {mathbb {R}})</span>, and <span>(eta _D)</span> admits a meromorphic continuation to <span>({mathbb {C}})</span>. We obtain some conditions of the frequencies <span>(lambda _n)</span> and some sums of coefficients <span>(a_n)</span> which imply that <span>(eta _D)</span> cannot be prolonged as an entire function.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 2","pages":"201 - 212"},"PeriodicalIF":0.5,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Abelian (p)-groups with a fixed elementary subgroup or with a fixed elementary quotient Abelian (p) -具有固定初等子群或固定初等商的群
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-09 DOI: 10.1007/s00013-025-02150-w
Justyna Kosakowska, Markus Schmidmeier, Martin Schreiner
{"title":"Abelian (p)-groups with a fixed elementary subgroup or with a fixed elementary quotient","authors":"Justyna Kosakowska,&nbsp;Markus Schmidmeier,&nbsp;Martin Schreiner","doi":"10.1007/s00013-025-02150-w","DOIUrl":"10.1007/s00013-025-02150-w","url":null,"abstract":"<div><p>In his 1934 paper, G. Birkhoff poses the problem of classifying pairs (<i>G</i>, <i>U</i>) where <i>G</i> is an abelian group and <span>(Usubset G)</span> a subgroup, up to automorphisms of <i>G</i>. In general, Birkhoff’s problem is not considered feasible. In this note, we fix a prime number <i>p</i> and assume that <i>G</i> is a direct sum of cyclic <i>p</i>-groups and <span>(Usubset G)</span> is a subgroup. Under the assumption that the factor group <i>G</i>/<i>U</i> is an elementary abelian <i>p</i>-group, we show that the pair (<i>G</i>, <i>U</i>) always has a direct sum decomposition into pairs of type <span>(({mathbb {Z}}/(p^n),{mathbb {Z}}/(p^n)))</span> or <span>((mathbb {Z}/(p^n), (p)))</span>. Surprisingly, in the dual situation, we need an additional condition. If we assume that <i>U</i> itself is an elementary subgroup of <i>G</i>, then we show that the pair (<i>G</i>, <i>U</i>) has a direct sum decomposition into pairs of type <span>(({mathbb {Z}}/(p^n),0))</span> or <span>((mathbb {Z}/(p^n), (p^{n-1})))</span> if and only if <i>G</i>/<i>U</i> is a direct sum of cyclic <i>p</i>-groups. We generalize the above results to modules over commutative discrete valuation rings.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 3","pages":"235 - 246"},"PeriodicalIF":0.5,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02150-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Laplacians and the disorientability of a simplicial complex 论拉普拉斯学派与单纯复合体的失向性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-09 DOI: 10.1007/s00013-025-02146-6
R. Balaji, Gargi Lather, Vinayak Gupta
{"title":"On Laplacians and the disorientability of a simplicial complex","authors":"R. Balaji,&nbsp;Gargi Lather,&nbsp;Vinayak Gupta","doi":"10.1007/s00013-025-02146-6","DOIUrl":"10.1007/s00013-025-02146-6","url":null,"abstract":"<div><p>Let <i>K</i> be an <i>N</i>-dimensional simplicial complex. We investigate the spectrum of the up Laplacian matrix of <i>K</i>. Let <i>L</i> be the <span>((N-1))</span>th up Laplacian matrix of <i>K</i>. We show that the largest eigenvalues of <i>L</i> and |<i>L</i>| are equal if and only if <i>K</i> is disorientable. We also derive lower bounds for the sum of the first <i>k</i> largest eigenvalues of <i>L</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 4","pages":"379 - 388"},"PeriodicalIF":0.5,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Infinitely many counterexamples of a conjecture of Franušić and Jadrijević Franušić和jadrijeviki猜想的无限反例
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-07 DOI: 10.1007/s00013-025-02144-8
Shubham Gupta
{"title":"Infinitely many counterexamples of a conjecture of Franušić and Jadrijević","authors":"Shubham Gupta","doi":"10.1007/s00013-025-02144-8","DOIUrl":"10.1007/s00013-025-02144-8","url":null,"abstract":"<div><p>Let <i>d</i> be a square-free integer such that <span>(d equiv 15 pmod {60})</span> and Pell’s equation <span>(x^2 - dy^2 = -6)</span> is solvable in rational integers <i>x</i> and <i>y</i>. In this paper, we prove that there exist infinitely many Diophantine quadruples in <span>(mathbb {Z}[sqrt{d}])</span> with the property <i>D</i>(<i>n</i>) for certain <i>n</i>’s. As an application of it, we ‘unconditionally’ prove the existence of infinitely many rings <span>(mathbb {Z}[sqrt{d}])</span> for which the conjecture of Franušić and Jadrijević (Conjecture 1.1) does ‘not’ hold. This conjecture states a relationship between the existence of a Diophantine quadruple in <span>(mathcal {R})</span> with the property <i>D</i>(<i>n</i>) and the representability of <i>n</i> as a difference of two squares in <span>(mathcal {R})</span>, where <span>(mathcal {R})</span> is a commutative ring with unity.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 2","pages":"173 - 184"},"PeriodicalIF":0.5,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 perfect symmetric rank-metric codes 关于完全对称秩-度量码
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-07 DOI: 10.1007/s00013-025-02145-7
Usman Mushrraf, Ferdinando Zullo
{"title":"On perfect symmetric rank-metric codes","authors":"Usman Mushrraf,&nbsp;Ferdinando Zullo","doi":"10.1007/s00013-025-02145-7","DOIUrl":"10.1007/s00013-025-02145-7","url":null,"abstract":"<div><p>Let <span>(textrm{Sym}_q(m))</span> be the space of symmetric matrices in <span>({mathbb {F}}_q^{mtimes m})</span>. A subspace of <span>(textrm{Sym}_q(m))</span> equipped with the rank distance is called an <span>({{mathbb {F}}}_{q})</span>-linear symmetric rank-metric code. In this paper, we study the covering properties of <span>({{mathbb {F}}}_{q})</span>-linear symmetric rank-metric codes. First we characterize <span>({{mathbb {F}}}_{q})</span>-linear symmetric rank-metric codes which are perfect, i.e., that satisfy the equality in the sphere-packing like bound. We show that, despite the rank-metric case, there are non-trivial perfect codes. Indeed, we prove that the only perfect non-trivial <span>({{mathbb {F}}}_{q})</span>-linear symmetric rank-metric codes in <span>(textrm{Sym}_q(m))</span> are the symmetric MRD codes with minimum distance 3 and <i>m</i> odd. Also, we characterize families of codes which are quasi-perfect.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 3","pages":"259 - 271"},"PeriodicalIF":0.5,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The Brylinski beta function of a coaxial layer 同轴层的Brylinski beta函数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-07-04 DOI: 10.1007/s00013-025-02138-6
Pooja Rani, M. K. Vemuri
{"title":"The Brylinski beta function of a coaxial layer","authors":"Pooja Rani,&nbsp;M. K. Vemuri","doi":"10.1007/s00013-025-02138-6","DOIUrl":"10.1007/s00013-025-02138-6","url":null,"abstract":"<div><p>In (Differential Geom. Appl. 92: Paper No. 102078, 12 pp., 2024), an analogue of Brylinski’s knot beta function was defined for a compactly supported (Schwartz) distribution <i>T</i> on Euclidean space. Here we consider the Brylinski beta function of the distribution defined by a coaxial layer on a submanifold of Euclidean space. We prove that it has an analytic continuation to the whole complex plane as a meromorphic function with only simple poles, and in the case of a coaxial layer on a space curve, we compute some of the residues in terms of the curvature and torsion.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 2","pages":"213 - 225"},"PeriodicalIF":0.5,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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