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Finite p-groups with cyclic center have non-inner automorphisms of order p 具有循环中心的有限p群具有p阶的非内自同构
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-19 DOI: 10.1007/s00013-025-02112-2
Mandeep Singh, Mahak Sharma
{"title":"Finite p-groups with cyclic center have non-inner automorphisms of order p","authors":"Mandeep Singh,&nbsp;Mahak Sharma","doi":"10.1007/s00013-025-02112-2","DOIUrl":"10.1007/s00013-025-02112-2","url":null,"abstract":"<div><p>Let <i>p</i> be a prime number. A longstanding conjecture asserts that every finite non-abelian <i>p</i>-group has a non-inner automorphism of order <i>p</i>. In this paper, under some conditions on an odd order finite <i>p</i>-group <i>G</i> with cyclic center, we prove that <i>G</i> exhibits a non-inner automorphism of order <i>p</i>. As a consequence, under certain conditions on a finite <i>p</i>-group <i>G</i> <span>((p&gt;2),)</span> the conjecture is proved for all nilpotency classes except class 2 and maximal class. Moreover, we also settle the conjecture for some non-abelian finite 3-groups of coclass 3,  which is a pending case of the main result of Ruscitti et al. (Monatsh. Math. 183(4):679–697, 2016).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"469 - 474"},"PeriodicalIF":0.5,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818315","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
Polynomial images of structured sets 结构化集合的多项式图像
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-13 DOI: 10.1007/s00013-025-02113-1
Bogdan Nica
{"title":"Polynomial images of structured sets","authors":"Bogdan Nica","doi":"10.1007/s00013-025-02113-1","DOIUrl":"10.1007/s00013-025-02113-1","url":null,"abstract":"<div><p>We extend results on value sets of polynomials over finite fields to polynomial images of ‘structured’ finite sets.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"503 - 509"},"PeriodicalIF":0.5,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818196","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 Bloom-type estimates for commutators of the fractional maximal function 分数极大函数对易子的bloom型估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-12 DOI: 10.1007/s00013-025-02111-3
Jie Sun, Jianglong Wu, Pu Zhang
{"title":"On Bloom-type estimates for commutators of the fractional maximal function","authors":"Jie Sun,&nbsp;Jianglong Wu,&nbsp;Pu Zhang","doi":"10.1007/s00013-025-02111-3","DOIUrl":"10.1007/s00013-025-02111-3","url":null,"abstract":"<div><p>Let <span>(0&lt;alpha &lt;n)</span> and <span>(M_{alpha })</span> be the fractional maximal function. For a locally integrable function <i>b</i>, we denote by <span>(M_{alpha ,b})</span> and <span>([b,M_{alpha }])</span> the maximal commutator and the commutator of <span>(M_{alpha })</span> with <i>b</i>. In this paper, we consider Bloom-type estimates for <span>(M_{alpha ,b})</span> and <span>([b,M_{alpha }])</span>. Some necessary and sufficient conditions to characterize the Bloom-type two-weight norm inequalities are given.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"661 - 673"},"PeriodicalIF":0.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084983","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
Integral Cayley graphs over a finite symmetric algebra 有限对称代数上的Cayley图积分
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-11 DOI: 10.1007/s00013-025-02108-y
Tung T. Nguyen, Nguyễn Duy Tân
{"title":"Integral Cayley graphs over a finite symmetric algebra","authors":"Tung T. Nguyen,&nbsp;Nguyễn Duy Tân","doi":"10.1007/s00013-025-02108-y","DOIUrl":"10.1007/s00013-025-02108-y","url":null,"abstract":"<div><p>A graph is called integral if its eigenvalues are integers. In this article, we provide necessary and sufficient conditions for a Cayley graph over a finite symmetric algebra <i>R</i> to be integral. This generalizes the work of So who studies the case where <i>R</i> is the ring of integers modulo <i>n</i>. We also explain some number-theoretic constructions of finite symmetric algebras arising from global fields, which we hope could pave the way for future studies on Paley graphs associated with finite Hecke characters.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"615 - 623"},"PeriodicalIF":0.5,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084981","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 embedding problem in algebras with involution 对合代数中的嵌入问题
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-10 DOI: 10.1007/s00013-025-02110-4
Jonatan Andres Gomez Parada
{"title":"The embedding problem in algebras with involution","authors":"Jonatan Andres Gomez Parada","doi":"10.1007/s00013-025-02110-4","DOIUrl":"10.1007/s00013-025-02110-4","url":null,"abstract":"<div><p>Let <i>K</i> be an algebraically closed field of characteristic zero, and let <i>A</i> and <i>B</i> be two simple algebras with involution over <i>K</i>. In this note, we study the embedding problem for algebras with involution. More specifically, if the algebra <i>A</i> satisfies the polynomial identities with involution of the algebra <i>B</i>, we investigate whether there exists an embedding of <i>A</i> into <i>B</i> that preserves the involutions.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"605 - 613"},"PeriodicalIF":0.5,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084916","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
Representations of extensions of simple groups 单群的扩展表示
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-08 DOI: 10.1007/s00013-025-02105-1
Scott Harper, Martin W. Liebeck
{"title":"Representations of extensions of simple groups","authors":"Scott Harper,&nbsp;Martin W. Liebeck","doi":"10.1007/s00013-025-02105-1","DOIUrl":"10.1007/s00013-025-02105-1","url":null,"abstract":"<div><p>Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group <i>G</i> factors through a projective representation of <i>G</i>, except for some groups of Lie type in characteristic 2; the exact exceptions for <i>G</i> were determined by Kleidman and Liebeck (1989). We generalise this result in two ways. First we consider all low-dimensional projective representations, not just those of minimal dimension. Second we consider all characteristically simple groups, not just simple groups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"365 - 375"},"PeriodicalIF":0.5,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02105-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622158","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
Continuity of the continued fraction mapping revisited 重新讨论连分数映射的连续性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-04 DOI: 10.1007/s00013-025-02102-4
Min Woong Ahn
{"title":"Continuity of the continued fraction mapping revisited","authors":"Min Woong Ahn","doi":"10.1007/s00013-025-02102-4","DOIUrl":"10.1007/s00013-025-02102-4","url":null,"abstract":"<div><p>The continued fraction mapping maps a number in the interval [0, 1) to the sequence of its partial quotients. When restricted to the set of irrationals, which is a subspace of the Euclidean space <span>(mathbb {R})</span>, the continued fraction mapping is a homeomorphism onto the product space <span>(mathbb {N}^{mathbb {N}})</span>, where <span>(mathbb {N})</span> is a discrete space. In this short note, we examine the continuity of the continued fraction mapping, addressing both irrational and rational points of the unit interval.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"395 - 405"},"PeriodicalIF":0.5,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622052","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
Two improved anisotropic Liouville type theorems for the stationary 3D Navier–Stokes equations 平稳三维Navier-Stokes方程的两个改进的各向异性Liouville型定理
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-04 DOI: 10.1007/s00013-025-02106-0
Zhibing Zhang, Qian Zu
{"title":"Two improved anisotropic Liouville type theorems for the stationary 3D Navier–Stokes equations","authors":"Zhibing Zhang,&nbsp;Qian Zu","doi":"10.1007/s00013-025-02106-0","DOIUrl":"10.1007/s00013-025-02106-0","url":null,"abstract":"<div><p>In this paper, we establish two new anisotropic Liouville type theorems for the stationary 3D Navier–Stokes equations. Under certain anisotropic integrability conditions on the components of the velocity, we show that the solution is trivial. Our results extend and improve the results of Chae (Appl Math Lett 142:108655, 2023) and Luo and Yin (Arch Ration Mech Anal 224:209–231, 2017).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"571 - 582"},"PeriodicalIF":0.5,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818133","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 endpoint estimates for pseudo-differential operators 伪微分算子的端点估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-03-01 DOI: 10.1007/s00013-025-02107-z
Guoning Wu, Jie Yang
{"title":"The endpoint estimates for pseudo-differential operators","authors":"Guoning Wu,&nbsp;Jie Yang","doi":"10.1007/s00013-025-02107-z","DOIUrl":"10.1007/s00013-025-02107-z","url":null,"abstract":"<div><p>Let <span>(T_{a})</span> be a pseudo-differential operator with symbol <i>a</i>. When <span>(ain S^m_{rho ,1},m=n(rho -1))</span>, it is well known that <span>(T_{a})</span> is not always bounded on <span>({L^1}({mathbb {R}^n}))</span>. However, under extra assumptions on <i>a</i>, we prove that <span>(T_{a})</span> is bounded on <span>({L^p}({mathbb {R}^n}))</span> for <span>(1 le p le infty )</span> when <span>(a in {L^infty }S_rho ^{n(rho - 1)}(omega ))</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"675 - 681"},"PeriodicalIF":0.5,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084797","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
A geodesic insight into some fundamental fusion theorems 对一些基本融合定理的测地线洞察
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-02-28 DOI: 10.1007/s00013-025-02101-5
M. Yasir Kızmaz
{"title":"A geodesic insight into some fundamental fusion theorems","authors":"M. Yasir Kızmaz","doi":"10.1007/s00013-025-02101-5","DOIUrl":"10.1007/s00013-025-02101-5","url":null,"abstract":"<div><p>Let <i>p</i> be an odd prime and <i>P</i> a Sylow <i>p</i>-subgroup of a finite group <i>G</i>. If <i>P</i> is either metacyclic or each of its elements of order <i>p</i> lies in the center, then <span>(N_G(P))</span> controls strong <i>G</i>-fusion in <i>P</i>, as established in Martino and Priddy (Math. Z. 225(2):277–288, 1997, Theorems 2.7 and 4.1). First, we provide alternative proofs for these results without relying on the Alperin fusion theorem, thereby simplifying the theoretical framework. Second, we establish an equivalence for the control of fusion in terms of a permutation character. Specifically, we define the permutation character induced by the action of <i>G</i> on <span>(Syl_p(G))</span> as <i>the Sylow </i><i>p</i><i>-character of</i> <i>G</i>. Now let <span>(Pin Syl_p(G))</span>, and <span>(N_G(P)le N le G )</span>. Set <span>(chi ,psi )</span> to be the Sylow <i>p</i>-characters of <i>G</i> and <i>N</i>, respectively. Then we prove that <i>N</i> controls <i>G</i>-fusion in <i>P</i> if and only if <span>(frac{chi (g)}{psi (g)}=frac{|C_G(g)|}{|C_N(g)|} text { for all } gin P.)</span> In the case that <i>N</i> is a <i>p</i>-local subgroup, further results are obtained.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"377 - 388"},"PeriodicalIF":0.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622106","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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