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A characterization of finite $sigma$-soluble $Psigma T$-groups 有限$sigma$-可溶$Psigma $-群的表征
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-12-20 DOI: 10.4171/rsmup/108
C. Cao, Dein Wong, Chi Zhang
{"title":"A characterization of finite $sigma$-soluble $Psigma T$-groups","authors":"C. Cao, Dein Wong, Chi Zhang","doi":"10.4171/rsmup/108","DOIUrl":"https://doi.org/10.4171/rsmup/108","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74110837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Huppert’s conjecture and almost simple groups 于佩尔猜想和几乎单群
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-12-01 DOI: 10.4171/rsmup/103
A. Daneshkhah
{"title":"Huppert’s conjecture and almost simple groups","authors":"A. Daneshkhah","doi":"10.4171/rsmup/103","DOIUrl":"https://doi.org/10.4171/rsmup/103","url":null,"abstract":"Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is H0 = PSL(2, q) with q = 2 f (f prime) such that cd(G) = cd(H), then there exists an abelian subgroup A of G such that G/A is isomorphic to H. In view of Huppert’s conjecture (2000), the main result of this paper gives rise to some examples that G is not necessarily a direct product of A and H, and consequently, we cannot extend this conjecture to almost simple groups. Mathematics Subject Classification (2010). Primary: 20C15; Secondary: 20D05","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78747197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Finite groups with $H_{mathcal L}$-embedded subgroups 嵌入$H_{mathcal L}$子群的有限群
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-12-01 DOI: 10.4171/rsmup/102
B. Hu, Jianhong Huang, A. Skiba
{"title":"Finite groups with $H_{mathcal L}$-embedded subgroups","authors":"B. Hu, Jianhong Huang, A. Skiba","doi":"10.4171/rsmup/102","DOIUrl":"https://doi.org/10.4171/rsmup/102","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76188611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Markov triples with two Fibonacci components 具有两个斐波那契分量的马尔可夫三元组
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-12-01 DOI: 10.4171/rsmup/99
F. Luca
{"title":"Markov triples with two Fibonacci components","authors":"F. Luca","doi":"10.4171/rsmup/99","DOIUrl":"https://doi.org/10.4171/rsmup/99","url":null,"abstract":"In this paper, we prove that there are at most finitely many pairs of Fibonacci numbers (x, y) = (Fm, Fn) with the property that m ≤ n and the pair (m,n) 6∈ {(1, 2r− 1), (1, 2), (2, 2r+ 1), (2r+ 1, 2r+ 3) : r ≥ 1} such that (x, y, z) is a Markov triple for some integer z. Mathematics Subject Classification (2010). Primary: 11B39; Secondary: 11D61.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84224067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-variational structure approach to systems with degenerate diffusions 退化扩散系统的拟变分结构方法
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-07-11 DOI: 10.4171/rsmup/96
A. Ito
{"title":"Quasi-variational structure approach to systems with degenerate diffusions","authors":"A. Ito","doi":"10.4171/rsmup/96","DOIUrl":"https://doi.org/10.4171/rsmup/96","url":null,"abstract":"We consider the following system (CA) consisting of one strongly nonlinear partial differential inclusion (PDI in short) with one linear PDE and one ODE, which describes a tumor invasion phenomenon with a haptotaxis effect and was originally proposed in [1]: (CA)  ut −∇ · (du(v)∇β(v ;w)− u∇λ(v)) + β(v ;u) ∋ 0, vt = −avw, wt = dw∆w − bw + cu. This system has two interesting characteristics. One is that the diffusion coefficient du for the unknown function u in the partial differential inclusion depends on the function v, which is also unknown in this system. The other is that the diffusion flux ∇β(v ;u) of u also depends on v. Moreover, we are especially interested in the case that β(v ;u) is nonsmooth and degenerate in general under suitable assumptions. These facts make it difficult for us to treat this system mathematically. In order to overcome these mathematical difficulties, we apply the theory of evolution inclusions on the real Hilbert space V ∗, the dual space of V , with a quasi-variational structure for the inner products, which is established in [8], and show the existence of time global solutions to the initial-boundary value problem for this system. Mathematics Subject Classification (2010). Primary: 34G25; Secondary: 47J35, 49J40, 58E35.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"110 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75975265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Torsors under abelian schemes via Picard schemes 通过Picard方案的abelian方案下的托子
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-07-11 DOI: 10.4171/rsmup/91
R. Lodh
{"title":"Torsors under abelian schemes via Picard schemes","authors":"R. Lodh","doi":"10.4171/rsmup/91","DOIUrl":"https://doi.org/10.4171/rsmup/91","url":null,"abstract":"Given a torsor P under a principally polarised abelian scheme J , projective over a noetherian base, we use the Picard scheme of P to write down an explicit extension of Z by J giving the class of P . As an application we give a version of Bhatt’s period-index result valid over an arbitrary noetherian base.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77783140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On log-growth of solutions of $p$-adic differential equations with $p$-adic exponents 带$p$进指数$p$进微分方程解的对数增长
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-07-11 DOI: 10.4171/rsmup/95
Takahiro Nakagawa
{"title":"On log-growth of solutions of $p$-adic differential equations with $p$-adic exponents","authors":"Takahiro Nakagawa","doi":"10.4171/rsmup/95","DOIUrl":"https://doi.org/10.4171/rsmup/95","url":null,"abstract":"We consider a differential system x d dxY = GY , where G is a m × m matrix whose coefficients are power series which converge and are bounded on the open unit disc D(0, 1−). Assume that G(0) is a diagonal matrix with p-adic integer coefficients. Then there exists a solution matrix of the form Y = F exp(G(0) log x) at x = 0 if all exponent differences are p-adically non-Liouville numbers. We give an example where F is analytic on the p-adic open unit disc and has log-growth greater than m. Under some conditions, we prove that if a solution matrix at a generic point has log-growth δ, then F has log-growth δ. Mathematics Subject Classification (2010). Primary: 12H25.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78490544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential 具有Riesz和背景势的非局部周长的极小值的不存在性
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-06-02 DOI: 10.4171/rsmup/93
F. Onoue
{"title":"Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential","authors":"F. Onoue","doi":"10.4171/rsmup/93","DOIUrl":"https://doi.org/10.4171/rsmup/93","url":null,"abstract":"We consider the nonexistence of minimizers for the energy containing a nonlocal perimeter with a general kernel K, a Riesz potential, and a background potential in R with N ≥ 2 under the volume constraint. We show that the energy has no minimizer for a sufficiently large volume under suitable assumptions on K. The proof is based on the partition of a minimizer and the comparison of the sum of the energy for each part with the energy for the original configuration. Mathematics Subject Classification (2010). 49J40, 49Q10, 49Q20, 28A75.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73643029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Bloch’s theorem for heat mappings 热映射的布洛赫定理
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-05-31 DOI: 10.4171/rsmup/92
J. Cortissoz
{"title":"Bloch’s theorem for heat mappings","authors":"J. Cortissoz","doi":"10.4171/rsmup/92","DOIUrl":"https://doi.org/10.4171/rsmup/92","url":null,"abstract":"In this paper we give a proof via the contraction mapping principle of a Bloch-type theorem for (normalised) heat Bochner-Takahashi K-mappings, that is, mappings that are solutions to the heat equation, and which also satisfy a weak form of K-quasiregularity. We also provide estimates from below for the radius of the univalent balls covered by this family of functions.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77535777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On join irreducible $J$-trivial semigroups 关于连接不可约$J$平凡半群
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-05-20 DOI: 10.4171/rsmup/90
Edmond W. H. Lee, J. Rhodes, B. Steinberg
{"title":"On join irreducible $J$-trivial semigroups","authors":"Edmond W. H. Lee, J. Rhodes, B. Steinberg","doi":"10.4171/rsmup/90","DOIUrl":"https://doi.org/10.4171/rsmup/90","url":null,"abstract":"A pseudovariety of semigroups is join irreducible if whenever it is contained in the complete join of some pseudovarieties, then it is contained in one of the pseudovarieties. A finite semigroup is join irreducible if it generates a join irreducible pseudovariety. New finite J -trivial semigroups Cn (n ≥ 2) are exhibited with the property that while each Cn is not join irreducible, the monoid C I n is join irreducible. The monoids Cn are the first examples of join irreducible J -trivial semigroups that generate pseudovarieties that are not self-dual. Several sufficient conditions are also established under which a finite semigroup is not join irreducible. Based on these results, join irreducible pseudovarieties generated by a J -trivial semigroup of order up to six are completely described. It turns out that besides known examples and those generated by C2 and its dual monoid, there are no further examples. Mathematics Subject Classification (2010). 20M07, 08B15.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75071740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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