Transactions of the American Mathematical Society, Series B最新文献_第3页

Correction to “A finite basis theorem for difference-term varieties with a finite residual bound” 对“残差界有限的差分项的有限基定理”的修正

Transactions of the American Mathematical Society, Series B

Pub Date : 2022-05-17 DOI: 10.1090/btran/120

K. Kearnes, Á. Szendrei, R. Willard

There is a gap in our proof [Trans. Amer. Math. Soc. 368 (2016), pp. 2115–2143, Lemma 6.2]. We direct readers to a paper that fills the gap.

我们的证明有漏洞[译]。阿米尔。数学。Soc. 368 (2016)， pp. 2115-2143，引理6.2]。我们引导读者去看一份能填补空白的报纸。

引用次数: 0

Pseudo-Anosov subgroups of general fibered 3–manifold groups 一般纤维3流形群的伪anosov子群

Transactions of the American Mathematical Society, Series B

Pub Date : 2022-04-08 DOI: 10.1090/btran/157

C. Leininger, Jacob Russell

We show that finitely generated and purely pseudo-Anosov subgroups of fundamental groups of fibered 3–manifolds with reducible monodromy are convex cocompact as subgroups of the mapping class group via the Birman exact sequence. Combined with results of Dowdall–Kent–Leininger and Kent–Leininger–Schleimer, this establishes the result for the image of all such fibered 3–manifold groups in the mapping class group.

通过Birman精确序列证明了具有可约单的纤维3流形的基本群的有限生成的纯伪anosov子群作为映射类群的子群是凸紧的。结合Dowdall-Kent-Leininger和Kent-Leininger-Schleimer的结果，建立了映射类群中所有这类光纤3流形群的像的结果。

引用次数: 1

Riesz and Green energy on projective spaces Riesz和绿色能源在投影空间

Transactions of the American Mathematical Society, Series B

Pub Date : 2022-04-08 DOI: 10.1090/btran/161

A. Anderson, M. Dostert, P. Grabner, Ryan Matzke, T. Stepaniuk

In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for the mentioned energies using determinantal point processes. Moreover, we determine lower bounds for these energies of the same order of magnitude.

本文研究两点齐次空间上的Riesz、Green和对数能量。更准确地说，我们考虑实数、复数、四元数和Cayley投影空间。对于这些空间中的每一个，我们使用行列式点过程提供了上述能量的上限估计。此外，我们确定了这些相同数量级的能量的下界。

引用次数: 4

Weak hypergraph regularity and applications to geometric Ramsey theory 弱超图正则性及其在几何Ramsey理论中的应用

Transactions of the American Mathematical Society, Series B

Pub Date : 2022-03-17 DOI: 10.1090/btran/61

N. Lyall, Á. Magyar

Let Δ = Δ 1 × … × Δ d ⊆ R n Delta =Delta _1times ldots times Delta _dsubseteq mathbb {R}^n , where R n = R n 1 × ⋯ × R n d mathbb {R}^n=mathbb {R}^{n_1}times cdots times mathbb {R}^{n_d} with each Δ

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引用次数: 15

The Legendre-Hardy inequality on bounded domains 有界域上的legende - hardy不等式

Transactions of the American Mathematical Society, Series B

Pub Date : 2022-03-17 DOI: 10.1090/btran/75

Jaeyoung Byeon, Sangdon Jin

There have been numerous studies on Hardy’s inequality on a bounded domain, which holds for functions vanishing on the boundary. On the other hand, the classical Legendre differential equation defined in an interval can be regarded as a Neumann version of the Hardy inequality with subcritical weight functions. In this paper we study a Neumann version of the Hardy inequality on a bounded C 2 C^2 -domain in R n mathbb {R}^n of the following form ∫ Ω d β ( x ) | ∇ u ( x ) | 2

Hardy在有界域上的不等式已经得到了大量的研究，该不等式适用于在边界上消失的函数。另一方面，定义在区间内的经典Legendre微分方程可以看作是具有次临界权函数的Hardy不等式的诺伊曼版本。本文研究了R n mathbb中有界C 2 C²定义域上Hardy不等式的一个诺伊曼版本，其形式为∫Ω d β (x) |∇u (x) | 2d x≥C (α，β)∫Ω | u (x) | 2d α (x) dx with∫Ω u (x)d α (x) d x = 0, {}begin{equation*} int _Omega d^{beta }(x) |nabla u(x) |^2 dx ge C(alpha ,beta ) int _Omega frac {|u(x)|^2}{d^{alpha }(x)} dx quad text { with }quad int _Omega frac {u(x)}{d^{alpha }(x)} dx=0, end{equation*}其中d(x) d(x)是x∈Ω x inOmega到边界∂Ω partialOmega和α， β∈R alpha的距离，betainmathbb我们对C(α， β) > 0 C({}alpha, beta) > 0的所有(α， β)∈r2 (alpha, beta) {}inmathbb R^2进行分类。然后，我们研究了是否获得最优常数C(α， β) C(alpha, beta)。我们对C (α

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引用次数: 1

Rank growth of elliptic curves over 𝑁-th root extensions 𝑁-th根扩展上椭圆曲线的秩生长

Transactions of the American Mathematical Society, Series B

Pub Date : 2021-12-23 DOI: 10.1090/btran/149

A. Shnidman, Ariel Weiss

Fix an elliptic curve E E over a number field F F and an integer n n which is a power of 3 3 . We study the growth of the Mordell–Weil rank of E E after base change to the fields K d = F ( d 2 n ) K_d = F(!sqrt [2n]{d}) . If E E admits a 3 3 -isogeny, then we show that the average “new rank” o

在一个数字域F F上固定一条椭圆曲线E E和一个整数n n是3的幂。我们研究了碱基改变后E E的modell - weil秩在K d = F(d 2n) K_d = F(!sqrt [2n]{d})。如果E - E有一个33 -等同基因，那么我们证明E - E / K - d - K_d的平均“新秩”，适当地定义，当d - d的高度趋于无穷时是有界的。当n = 3 n = 3时，我们进一步证明了对于许多椭圆曲线E/ Q E/mathbb {Q}，在E/ Q (d 6) mathbb {Q}(sqrt [6]d)上没有新的点，对于正比例的整数d d。这是Cornut和Vatsal [Rankin-Selberg l-函数和CM点的非平凡性，l-函数和伽罗瓦表示，卷320，剑桥大学出版社，剑桥，2007年，第121-186页]的一个著名结果的水平模拟。作为推论，我们证明了希尔伯特的第10问题在纯性域Q (d 6) mathbb {Q}(sqrt [6]{d})的正比例上有一个负解。证明结合了我们最近关于分环扭转族中阿贝尔变体的秩的工作和我们称之为“相关技巧”的技术，它适用于更一般的情况，即人们试图证明多个Selmer群同时消失。我们也将这一技术应用于Prym曲面的扭转族，得到了双椭圆格3曲线的六维扭转族中有理点个数的界。

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引用次数: 3

Congruences like Atkin’s for the partition function 像配分函数的阿特金同余

Transactions of the American Mathematical Society, Series B

Pub Date : 2021-12-17 DOI: 10.1090/btran/128

S. Ahlgren, P. Allen, S. Tang

Let p ( n ) p(n) be the ordinary partition function. In the 1960s Atkin found a number of examples of congruences of the form p ( Q 3 ℓ n + β ) ≡ 0 ( mod ℓ ) p( Q^3 ell n+beta )equiv 0pmod ell where ℓ ell and Q Q are prime and 5 ≤ ℓ ≤ 31 5leq ell leq 31 ; these lie in two natural families distinguished by the square class of

设p(n) p(n)是普通配分函数。在20世纪60年代，阿特金发现了一些形式为p(q3ln + β)≡0 (mod r) p(Q^3)的同余例子 ell n+beta ）equiv 0pmod ell 其中，l ell 和Q Q为素数，且5≤r≤31.5leq ell leq 31;它们属于两个自然族，由1−24 β (mod r) 1-24的平方类区分beta pmod ell ．在最近的几十年里，人们做了很多工作来理解形式为p(Q m ＿ n + β)≡0 (mod ＿ r) p(Q^m)的同余ell n+beta ）equiv 0pmod ell ．现在我们知道，当m≥4 m时，存在许多这样的同余geq 4，当m= 1,2 m= 1,2时，这样的同余是稀缺的(如果它们存在的话)，并且当m=0 m=0时，这样的同余仅在r = 5,7,11时存在 ell = 5,7,11。对于类似Atkin的同余式(当m=3 m=3时)，已经找到了更多的5≤r≤31.5的例子leq ell leq 但其他方面似乎知之甚少。这里我们利用模伽罗瓦表示理论证明了对于每一个素数≥5 ell geq 5，在阿特金发现的第一个自然族中有无限多个像阿特金那样的同余至少17/24的素数是17/24 ell 在第二族中有无限多个同余。

{"title":"Congruences like Atkin’s for the partition function","authors":"S. Ahlgren, P. Allen, S. Tang","doi":"10.1090/btran/128","DOIUrl":"https://doi.org/10.1090/btran/128","url":null,"abstract":"Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p left-parenthesis n right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">p(n)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be the ordinary partition function. In the 1960s Atkin found a number of examples of congruences of the form <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p left-parenthesis upper Q cubed script l n plus beta right-parenthesis identical-to 0 left-parenthesis mod script l right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msup>\u0000 <mml:mi>Q</mml:mi>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:msup>\u0000 <mml:mi>ℓ</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>β</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>≡</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mspace width=\"0.667em\" />\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>mod</mml:mi>\u0000 <mml:mspace width=\"0.333em\" />\u0000 <mml:mi>ℓ</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">p( Q^3 ell n+beta )equiv 0pmod ell</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script l\">\u0000 <mml:semantics>\u0000 <mml:mi>ℓ</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">ell</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Q\">\u0000 <mml:semantics>\u0000 <mml:mi>Q</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">Q</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> are prime and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"5 less-than-or-equal-to script l less-than-or-equal-to 31\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mn>5</mml:mn>\u0000 <mml:mo>≤</mml:mo>\u0000 <mml:mi>ℓ</mml:mi>\u0000 <mml:mo>≤</mml:mo>\u0000 <mml:mn>31</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">5leq ell leq 31</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>; these lie in two natural families distinguished by the square class of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1 minus 24 beta left-parenthesis mod script l right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 ","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121577100","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

The 𝐴₂ Andrews–Gordon identities and cylindric partitions 2 - Andrews-Gordon恒等式和柱面划分

Transactions of the American Mathematical Society, Series B

Pub Date : 2021-11-15 DOI: 10.1090/btran/147

S. Warnaar

Inspired by a number of recent papers by Corteel, Dousse, Foda, Uncu and Welsh on cylindric partitions and Rogers–Ramanujan-type identities, we obtain the A 2 mathrm {A}_2 (or A 2 ( 1 ) mathrm {A}_2^{(1)} ) analogues of the celebrated Andrews–Gordon identities. We further prove q q -series identities that correspond to the infinite-level limit of the Andrews–Gordon identities for A r − 1 mathrm {A}_{r-1} (or A r − 1 ( 1 )

受Corteel, Dousse, Foda, Uncu和Welsh最近关于圆柱划分和rogers - ramanujan型恒等式的一些论文的启发，我们得到了与著名的Andrews-Gordon恒等式类似的a2 mathm {a}_2(或a2 (1) mathm {a}_2^{(1)})。我们进一步证明了q q级数恒等式对应于任意秩rr的Andrews-Gordon恒等式的无穷级极限，即A r−1 mathm {A}_{r} -1}(或A r−1 (1) mathm {A}_{r-1}^{(1)})。我们对a2 maththrm {A}_2的结果也得出了对秩为33和阶为d d的圆柱形分区的22变量生成函数的推测性的、明显正的组合公式，使得d d不是33的倍数。

{"title":"The 𝐴₂ Andrews–Gordon identities and cylindric partitions","authors":"S. Warnaar","doi":"10.1090/btran/147","DOIUrl":"https://doi.org/10.1090/btran/147","url":null,"abstract":"Inspired by a number of recent papers by Corteel, Dousse, Foda, Uncu and Welsh on cylindric partitions and Rogers–Ramanujan-type identities, we obtain the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper A 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">A</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathrm {A}_2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> (or <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper A 2 Superscript left-parenthesis 1 right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:msubsup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">A</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:msubsup>\u0000 <mml:annotation encoding=\"application/x-tex\">mathrm {A}_2^{(1)}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>) analogues of the celebrated Andrews–Gordon identities. We further prove <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\">\u0000 <mml:semantics>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">q</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-series identities that correspond to the infinite-level limit of the Andrews–Gordon identities for <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper A Subscript r minus 1\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">A</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>r</mml:mi>\u0000 <mml:mo>−</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathrm {A}_{r-1}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> (or <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper A Subscript r minus 1 Superscript left-parenthesis 1 right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:msubsup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">A</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>r</mml:mi>\u0000 <mml:mo>−</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:msubsup>\u0000 <mml:ann","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124553895","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

Normal subgroups of big mapping class groups 大映射类群的正规子群

Transactions of the American Mathematical Society, Series B

Pub Date : 2021-10-15 DOI: 10.1090/btran/108

Danny Calegari, Lvzhou Chen

Let S S be a surface and let Mod ⁡ ( S , K ) operatorname {Mod}(S,K) be the mapping class group of S S permuting a Cantor subset K ⊂ S K subset S . We prove two structure theorems for normal subgroups of Mod ⁡ ( S , K ) operatorname {Mod}(S,K) .

(Purity:) if S S has finite type, every normal subgroup of Mod ⁡ ( S , K

设S S是一个曲面，设Mod (S,K) operatorname {Mod}(S,K)是S S置换康托尔子集K的映射类群;S K 子集S。我们证明了Mod (S,K) operatorname {Mod}(S,K)的正规子群的两个结构定理。(纯度:)如果S S具有有限类型，则Mod (S,K) operatorname {Mod}(S,K)的每个正规子群要么包含到S S的映射类群的遗忘映射的核，要么是'纯' -(惯性:)对于Cantor集合的任意n个元素子集Q Q，存在一个从纯子群PMod (S,K) operatorname {Mod}(S,K)到(S,Q) (S,Q)的映射类群(S,Q) (S,Q)的映射类群(S,Q)的映射，并定点地固定Q Q。如果N N是包含在PMod (S,K) operatorname {PMod}(S,K)中的Mod (S,K) operatorname {PMod}(S,K)的正规子群，那么它的像nqn_q同样是正规的。我们精确地描述了哪些有限型正规子群nqn_q是这样产生的。并给出了几个应用和大量的例子。

{"title":"Normal subgroups of big mapping class groups","authors":"Danny Calegari, Lvzhou Chen","doi":"10.1090/btran/108","DOIUrl":"https://doi.org/10.1090/btran/108","url":null,"abstract":"Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S\">\u0000 <mml:semantics>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">S</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be a surface and let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M o d left-parenthesis upper S comma upper K right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>Mod</mml:mi>\u0000 <mml:mo>⁡</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">operatorname {Mod}(S,K)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be the mapping class group of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S\">\u0000 <mml:semantics>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">S</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> permuting a Cantor subset <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K subset-of upper S\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mo>⊂</mml:mo>\u0000 <mml:mi>S</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">K subset S</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We prove two structure theorems for normal subgroups of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M o d left-parenthesis upper S comma upper K right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>Mod</mml:mi>\u0000 <mml:mo>⁡</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">operatorname {Mod}(S,K)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.\u0000\u0000(Purity:) if <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S\">\u0000 <mml:semantics>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">S</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> has finite type, every normal subgroup of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M o d left-parenthesis upper S comma upper K right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>Mod</mml:mi>\u0000 <mml:mo>⁡</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>K","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121640041","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: 11

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