Pub Date : 2023-09-15DOI: 10.1017/s1446788723000095
HENRIQUE F. DE LIMA, WALLACE F. GOMES, MÁRCIO S. SANTOS, MARCO ANTONIO L. VELÁSQUEZ
Abstract We investigate geometric aspects of complete spacelike mean curvature flow solitons of codimension one in a generalized Robertson–Walker (GRW) spacetime $-Itimes _{f}M^n$ , with base $Isubset mathbb R$ , Riemannian fiber $M^n$ and warping function $fin C^infty (I)$ . For this, we apply suitable maximum principles to guarantee that such a mean curvature flow soliton is a slice of the ambient space and to obtain nonexistence results concerning these solitons. In particular, we deal with entire graphs constructed over the Riemannian fiber $M^n$ , which are spacelike mean curvature flow solitons, and we also explore the geometry of a conformal vector field to establish topological and further rigidity results for compact (without boundary) mean curvature flow solitons in a GRW spacetime. Moreover, we study the stability of spacelike mean curvature flow solitons with respect to an appropriate stability operator. Standard examples of spacelike mean curvature flow solitons in GRW spacetimes are exhibited, and applications related to these examples are given.
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Pub Date : 2023-09-11DOI: 10.1017/s1446788722000325
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
{"title":"JAZ volume 115 issue 2 Cover and Front matter","authors":"","doi":"10.1017/s1446788722000325","DOIUrl":"https://doi.org/10.1017/s1446788722000325","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135980382","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}
Pub Date : 2023-09-11DOI: 10.1017/s1446788722000337
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
{"title":"JAZ volume 115 issue 2 Cover and Back matter","authors":"","doi":"10.1017/s1446788722000337","DOIUrl":"https://doi.org/10.1017/s1446788722000337","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135980441","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}
Pub Date : 2023-07-24DOI: 10.1017/s1446788723000071
F. de Giovanni, M. Trombetti, B. Wehrfritz
A well-known theorem of Philip Hall states that if a group G has a nilpotent normal subgroup N such that $G/N'$ is nilpotent, then G itself is nilpotent. We say that a group class 𝔛 is a Hall class if it contains every group G admitting a nilpotent normal subgroup N such that $G/N'$ belongs to 𝔛. Hall classes have been considered by several authors, such as Plotkin [‘Some properties of automorphisms of nilpotent groups’, Soviet Math. Dokl.2 (1961), 471–474] and Robinson [‘A property of the lower central series of a group’, Math. Z.107 (1968), 225–231]. A further detailed study of Hall classes is performed by us in another paper [‘Hall classes of groups’, to appear] and we also investigate the behaviour of the class of finite-by-𝔜 groups for a given Hall class 𝔜 [‘Hall classes in linear groups’, to appear]. The aim of this paper is to prove that for most natural choices of the Hall class 𝔜, also the classes $(mathbf{L}mathfrak{F})mathfrak{Y}$ and 𝔅𝔜 are Hall classes, where L𝔉 is the class of locally finite groups and 𝔅 is the class of locally finite groups of finite exponent.
Philip Hall的一个著名定理指出，如果群G有一个幂零的正规子群N，使得$G/N'$为幂零，则G本身为幂零。我们说一个群类𝔛是一个Hall类，如果它包含所有群G承认一个幂零正规子群N，使得$G/N'$属于𝔛。霍尔类已经被一些作者考虑过，如Plotkin['幂零群的自同构的一些性质'，苏联数学]。dokl2(1961)， 471-474]和Robinson['群的下中心级数的一个性质'，数学。[j].地球物理学报，1998,22(4):387 - 391。我们在另一篇论文['群的霍尔类'，即将出现]中对霍尔类进行了进一步的详细研究，我们还研究了有限by-𝔜类对于给定霍尔类𝔜的行为['线性群中的霍尔类'，即将出现]。本文的目的是证明对于Hall类𝔜的大多数自然选择，$(mathbf{L}mathfrak{F})mathfrak{Y}$和𝔜也是Hall类，其中L𝔉是局部有限群的类，是有限指数的局部有限群的类。
{"title":"HALL CLASSES OF GROUPS WITH A LOCALLY FINITE OBSTRUCTION","authors":"F. de Giovanni, M. Trombetti, B. Wehrfritz","doi":"10.1017/s1446788723000071","DOIUrl":"https://doi.org/10.1017/s1446788723000071","url":null,"abstract":"\u0000 A well-known theorem of Philip Hall states that if a group G has a nilpotent normal subgroup N such that \u0000 \u0000 \u0000 \u0000$G/N'$\u0000\u0000 \u0000 is nilpotent, then G itself is nilpotent. We say that a group class 𝔛 is a Hall class if it contains every group G admitting a nilpotent normal subgroup N such that \u0000 \u0000 \u0000 \u0000$G/N'$\u0000\u0000 \u0000 belongs to 𝔛. Hall classes have been considered by several authors, such as Plotkin [‘Some properties of automorphisms of nilpotent groups’, Soviet Math. Dokl.2 (1961), 471–474] and Robinson [‘A property of the lower central series of a group’, Math. Z.107 (1968), 225–231]. A further detailed study of Hall classes is performed by us in another paper [‘Hall classes of groups’, to appear] and we also investigate the behaviour of the class of finite-by-𝔜 groups for a given Hall class 𝔜 [‘Hall classes in linear groups’, to appear]. The aim of this paper is to prove that for most natural choices of the Hall class 𝔜, also the classes \u0000 \u0000 \u0000 \u0000$(mathbf{L}mathfrak{F})mathfrak{Y}$\u0000\u0000 \u0000 and 𝔅𝔜 are Hall classes, where L𝔉 is the class of locally finite groups and 𝔅 is the class of locally finite groups of finite exponent.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"45 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88889726","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}
Pub Date : 2023-07-18DOI: 10.1017/s144678872300006x
Tapendu Rana
We prove Wiener Tauberian theorem type results for various spaces of radial functions, which are Banach algebras on a real-rank-one semisimple Lie group G. These are natural generalizations of the Wiener Tauberian theorem for the commutative Banach algebra of the integrable radial functions on G.
{"title":"WIENER TAUBERIAN THEOREMS FOR CERTAIN BANACH ALGEBRAS ON REAL RANK ONE SEMISIMPLE LIE GROUPS","authors":"Tapendu Rana","doi":"10.1017/s144678872300006x","DOIUrl":"https://doi.org/10.1017/s144678872300006x","url":null,"abstract":"\u0000 We prove Wiener Tauberian theorem type results for various spaces of radial functions, which are Banach algebras on a real-rank-one semisimple Lie group G. These are natural generalizations of the Wiener Tauberian theorem for the commutative Banach algebra of the integrable radial functions on G.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"7 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85815482","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}
Pub Date : 2023-07-17DOI: 10.1017/s1446788722000313
{"title":"JAZ volume 115 issue 1 Cover and Back matter","authors":"","doi":"10.1017/s1446788722000313","DOIUrl":"https://doi.org/10.1017/s1446788722000313","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"33 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87960392","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}
Pub Date : 2023-07-17DOI: 10.1017/s1446788722000301
{"title":"JAZ volume 115 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s1446788722000301","DOIUrl":"https://doi.org/10.1017/s1446788722000301","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"5 1","pages":"f1 - f2"},"PeriodicalIF":0.7,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76831243","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}
Pub Date : 2023-05-29DOI: 10.1017/s1446788723000034
Lea Beneish, Debanjana Kundu, Anwesh Ray
Let p be a prime. In this paper, we use techniques from Iwasawa theory to study questions about rank jump of elliptic curves in cyclic extensions of degree p. We also study growth of the p-primary Selmer group and the Shafarevich–Tate group in cyclic degree-p extensions and improve upon previously known results in this direction.
{"title":"RANK JUMPS AND GROWTH OF SHAFAREVICH–TATE GROUPS FOR ELLIPTIC CURVES IN -EXTENSIONS","authors":"Lea Beneish, Debanjana Kundu, Anwesh Ray","doi":"10.1017/s1446788723000034","DOIUrl":"https://doi.org/10.1017/s1446788723000034","url":null,"abstract":"\u0000 Let p be a prime. In this paper, we use techniques from Iwasawa theory to study questions about rank jump of elliptic curves in cyclic extensions of degree p. We also study growth of the p-primary Selmer group and the Shafarevich–Tate group in cyclic degree-p extensions and improve upon previously known results in this direction.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"59 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73538715","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}
Pub Date : 2023-05-12DOI: 10.1017/s1446788722000271
{"title":"JAZ volume 114 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s1446788722000271","DOIUrl":"https://doi.org/10.1017/s1446788722000271","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"27 1","pages":"f1 - f2"},"PeriodicalIF":0.7,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81187626","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}
Pub Date : 2023-05-12DOI: 10.1017/s1446788722000283
{"title":"JAZ volume 114 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s1446788722000283","DOIUrl":"https://doi.org/10.1017/s1446788722000283","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"51 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83672973","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}
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