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Structure of finite groups with restrictions on the set of conjugacy classes sizes 具有共轭类大小集限制的有限群的结构
Communications in Mathematics Pub Date : 2022-06-20 DOI: 10.46298/cm.9722
I. Gorshkov
{"title":"Structure of finite groups with restrictions on the set of conjugacy classes sizes","authors":"I. Gorshkov","doi":"10.46298/cm.9722","DOIUrl":"https://doi.org/10.46298/cm.9722","url":null,"abstract":"Let $N(G)$ be the set of conjugacy classes sizes of $G$. We prove that if\u0000$N(G)=Omegatimes {1,n}$ for specific set $Omega$ of integers, then\u0000$Gsimeq Atimes B$ where $N(A)=Omega$, $N(B)={1,n}$, and $n$ is a power of\u0000prime.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45530861","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
Quasi Yamabe Solitons on 3-Dimensional Contact Metric Manifolds with Qvarphi=varphi Q Qvarphi=varphi Q的三维接触度量流形上的拟Yamabe孤子
Communications in Mathematics Pub Date : 2022-06-10 DOI: 10.46298/cm.9695
V. Venkatesha, H. Kumara
{"title":"Quasi Yamabe Solitons on 3-Dimensional Contact Metric Manifolds with Qvarphi=varphi Q","authors":"V. Venkatesha, H. Kumara","doi":"10.46298/cm.9695","DOIUrl":"https://doi.org/10.46298/cm.9695","url":null,"abstract":"In this paper we initiate the study of quasi Yamabe soliton on 3-dimensional\u0000contact metric manifold with Qvarphi=varphi Q and prove that if a\u00003-dimensional contact metric manifold M such that Qvarphi=varphi Q admits a\u0000quasi Yamabe soliton with non-zero soliton vector field V being point-wise\u0000collinear with the Reeb vector field {xi}, then V is a constant multiple of\u0000{xi}, the scalar curvature is constant and the manifold is Sasakian. Moreover,\u0000V is Killing. Finally, we prove that if M is a 3-dimensional compact contact\u0000metric manifold such that Qvarphi=varphi Q endowed with a quasi Yamabe\u0000soliton, then either M is flat or soliton is trivial.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46923967","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
Various notions of (co)simplicial (pre)sheaves （共）单纯（预）槽轮的各种概念
Communications in Mathematics Pub Date : 2022-05-30 DOI: 10.46298/cm.10359
Timothy Hosgood
{"title":"Various notions of (co)simplicial (pre)sheaves","authors":"Timothy Hosgood","doi":"10.46298/cm.10359","DOIUrl":"https://doi.org/10.46298/cm.10359","url":null,"abstract":"The phrase \"(co)simplicial (pre)sheaf\" can be reasonably interpreted in\u0000multiple ways. In this survey we study how the various notions familiar to the\u0000author relate to one another. We end by giving some example applications of the\u0000most general of these notions.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43102193","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
Non-split supermanifolds associated with the cotangent bundle 与余切束相关联的非分裂超流形
Communications in Mathematics Pub Date : 2022-05-24 DOI: 10.46298/cm.9613
A. Onishchik
{"title":"Non-split supermanifolds associated with the cotangent bundle","authors":"A. Onishchik","doi":"10.46298/cm.9613","DOIUrl":"https://doi.org/10.46298/cm.9613","url":null,"abstract":"Here, I study the problem of classification of non-split supermanifolds\u0000having as retract the split supermanifold $(M,Omega)$, where $Omega$ is the\u0000sheaf of holomorphic forms on a given complex manifold $M$ of dimension $> 1$.\u0000I propose a general construction associating with any $d$-closed $(1,1)$-form\u0000$omega$ on $M$ a supermanifold with retract $(M,Omega)$ which is non-split\u0000whenever the Dolbeault class of $omega$ is non-zero. In particular, this gives\u0000a non-empty family of non-split supermanifolds for any flag manifold $Mne\u0000mathbb{CP}^1$. In the case where $M$ is an irreducible compact Hermitian\u0000symmetric space, I get a complete classification of non-split supermanifolds\u0000with retract $(M,Omega)$. For each of these supermanifolds, the 0- and\u00001-cohomology with values in the tangent sheaf are calculated. As an example, I\u0000study the $Pi$-symmetric super-Grassmannians introduced by Yu. Manin.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42483634","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: 5
Invariance analysis and some new exact analytic solutions of the time-fractional coupled Drinfeld-Sokolov-Wilson equations 时间分数耦合Drinfeld-Sokolov-Wilson方程的不变性分析和一些新的精确解析解
Communications in Mathematics Pub Date : 2022-05-12 DOI: 10.46298/cm.9283
Chauhan Astha, Arora Rajan
{"title":"Invariance analysis and some new exact analytic solutions of the time-fractional coupled Drinfeld-Sokolov-Wilson equations","authors":"Chauhan Astha, Arora Rajan","doi":"10.46298/cm.9283","DOIUrl":"https://doi.org/10.46298/cm.9283","url":null,"abstract":"In this work, the fractional Lie symmetry method is used to find the exact solutions of the time-fractional coupled Drinfeld-Sokolov-Wilson equations with the Riemann-Liouville fractional derivative. Time-fractional coupled Drinfeld-Sokolov-Wilson equations are obtained by replacing the first-order time derivative to the fractional derivatives (FD) of order $alpha$ in the classical Drinfeld-Sokolov-Wilson (DSW) model. Using the fractional Lie symmetry method, the Lie symmetry generators are obtained. With the help of symmetry generators, FCDSW equations are reduced into fractional ordinary differential equations (FODEs) with Erd$acute{e}$lyi-Kober fractional differential operator. Also, we have obtained the exact solution of FCDSW equations and shown the effects of non-integer order derivative value on the solutions graphically. The effect of fractional order $alpha$ on the behavior of solutions is studied graphically. Finally, new conservation laws are constructed along with the formal Lagrangian and fractional generalization of Noether operators. It is quite interesting the exact analytic solutions are obtained in explicit form.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43657614","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
Computing subalgebras and $mathbb{Z}_2$-gradings of simple Lie algebras over finite fields 计算子代数和有限域上简单李代数的$mathbb{Z}_2$-分级
Communications in Mathematics Pub Date : 2022-05-06 DOI: 10.46298/cm.10193
B. Eick, T. Moede
{"title":"Computing subalgebras and $mathbb{Z}_2$-gradings of simple Lie algebras over finite fields","authors":"B. Eick, T. Moede","doi":"10.46298/cm.10193","DOIUrl":"https://doi.org/10.46298/cm.10193","url":null,"abstract":"This paper introduces two new algorithms for Lie algebras over finite fields\u0000and applies them to the investigate the known simple Lie algebras of dimension\u0000at most $20$ over the field $mathbb{F}_2$ with two elements. The first\u0000algorithm is a new approach towards the construction of $mathbb{Z}_2$-gradings\u0000of a Lie algebra over a finite field of characteristic $2$. Using this, we\u0000observe that each of the known simple Lie algebras of dimension at most $20$\u0000over $mathbb{F}_2$ has a $mathbb{Z}_2$-grading and we determine the\u0000associated simple Lie superalgebras. The second algorithm allows us to compute\u0000all subalgebras of a Lie algebra over a finite field. We apply this to compute\u0000the subalgebras, the maximal subalgebras and the simple subquotients of the\u0000known simple Lie algebras of dimension at most $16$ over $mathbb{F}_2$ (with\u0000the exception of the $15$-dimensional Zassenhaus algebra).","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45708605","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
Transitive irreducible Lie superalgebras of vector fields 向量场的传递不可约李超代数
Communications in Mathematics Pub Date : 2022-04-23 DOI: 10.46298/cm.10456
A. Onishchik
{"title":"Transitive irreducible Lie superalgebras of vector fields","authors":"A. Onishchik","doi":"10.46298/cm.10456","DOIUrl":"https://doi.org/10.46298/cm.10456","url":null,"abstract":"Let $mathfrak{d}$ be the Lie superalgebra of superderivations of the sheaf\u0000of sections of the exterior algebra of the homogeneous vector bundle $E$ over\u0000the flag variety $G/P$, where $G$ is a simple finite-dimensional complex Lie\u0000group and $P$ its parabolic subgroup. Then, $mathfrak{d}$ is transitive and\u0000irreducible whenever $E$ is defined by an irreducible $P$-module $V$ such that\u0000the highest weight of $V^*$ is dominant. Moreover, $mathfrak{d}$ is simple; it\u0000is isomorphic to the Lie superalgebra of vector fields on the superpoint, i.e.,\u0000on a $0|n$-dimensional supervariety.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44022356","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
Action of vectorial Lie superalgebras on some split supermanifolds 向量李超代数对某些分裂超流形的作用
Communications in Mathematics Pub Date : 2022-04-23 DOI: 10.46298/cm.10455
A. Onishchik
{"title":"Action of vectorial Lie superalgebras on some split supermanifolds","authors":"A. Onishchik","doi":"10.46298/cm.10455","DOIUrl":"https://doi.org/10.46298/cm.10455","url":null,"abstract":"The \"curved\" super Grassmannian is the supervariety of subsupervarieties of\u0000purely odd dimension $k$ in a~supervariety of purely odd dimension $n$, unlike\u0000the \"usual\" super Grassmannian which is the supervariety of linear\u0000subsuperspacies of purely odd dimension $k$ in a~superspace of purely odd\u0000dimension $n$. The Lie superalgebras of all and Hamiltonian vector fields on\u0000the superpoint are realized as Lie superalgebras of derivations of the\u0000structure sheaves of certain \"curved\" super Grassmannians,","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42132168","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
On commutativity of 3-prime near-rings with generalized (α; β)-derivations 具有广义(α)的3素数近环的交换性β)派生
Communications in Mathematics Pub Date : 2022-04-06 DOI: 10.46298/cm.9076
Abdelkarim BOUA, Ahmed Abdelwanis
{"title":"On commutativity of 3-prime near-rings with generalized (α; β)-derivations","authors":"Abdelkarim BOUA, Ahmed Abdelwanis","doi":"10.46298/cm.9076","DOIUrl":"https://doi.org/10.46298/cm.9076","url":null,"abstract":"Let (mathcal{N}) be a~(3)-prime near ring and (alpha,beta: mathcal{N}rightarrow mathcal{N}) be endomorphisms. In the present paper we amplify a~few outcomes concerning generalized derivations and two-sided (alpha)-generalized derivations of (3)-prime near rings to generalized ((alpha,beta))-derivations. Cases demonstrating the need of the (3)-primeness speculation are given. When (beta = id_{mathcal{N}}) (resp. (alpha = beta = id_{mathcal{N}})), one can easily obtain the main results of~cite{ref1} (resp.cite{ref5}).","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44369797","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
An existence result for $p$-Laplace equation with gradient nonlinearity in $mathbb{R}^N$ $mathbb{R}^N$中具有梯度非线性的$p$-拉普拉斯方程的存在性结果
Communications in Mathematics Pub Date : 2022-04-06 DOI: 10.46298/cm.9316
Shilpa Gupta, G. Dwivedi
{"title":"An existence result for $p$-Laplace equation with gradient nonlinearity\u0000 in $mathbb{R}^N$","authors":"Shilpa Gupta, G. Dwivedi","doi":"10.46298/cm.9316","DOIUrl":"https://doi.org/10.46298/cm.9316","url":null,"abstract":"We prove the existence of a weak solution to the problem begin{equation*}\u0000begin{split} -Delta_{p}u+V(x)|u|^{p-2}u & =f(u,|nabla u|^{p-2}nabla u), \u0000 u(x) & >0 forall xinmathbb{R}^{N}, end{split} end{equation*} where\u0000$Delta_{p}u=hbox{div}(|nabla u|^{p-2}nabla u)$ is the $p$-Laplace operator,\u0000$1<p<N$ and the nonlinearity\u0000$f:mathbb{R}timesmathbb{R}^{N}rightarrowmathbb{R}$ is continuous and it\u0000depends on gradient of the solution. We use an iterative technique based on the\u0000Mountain pass theorem to prove our existence result.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48145521","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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