Bulletin of the Australian Mathematical Society最新文献_第6页

MAXIMAL SUBSEMIGROUPS OF INFINITE SYMMETRIC GROUPS 无限对称群的最大子群

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-29 DOI: 10.1017/s0004972723001375

SUZANA MENDES-GONÇALVES, R. P. SULLIVAN

{"title":"MAXIMAL SUBSEMIGROUPS OF INFINITE SYMMETRIC GROUPS","authors":"SUZANA MENDES-GONÇALVES, R. P. SULLIVAN","doi":"10.1017/s0004972723001375","DOIUrl":"https://doi.org/10.1017/s0004972723001375","url":null,"abstract":"Brazil et al. [‘Maximal subgroups of infinite symmetric groups’, Proc. Lond. Math. Soc. (3)68(1) (1994), 77–111] provided a new family of maximal subgroups of the symmetric group $G(X)$ defined on an infinite set X. It is easy to see that, in this case, $G(X)$ contains subsemigroups that are not groups, but nothing is known about nongroup maximal subsemigroups of $G(X)$ . We provide infinitely many examples of such semigroups.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139586222","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 THE CHARACTERISATION OF ALTERNATING GROUPS BY CODEGREES 关于交替群的编码度特征

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-26 DOI: 10.1017/s0004972723001429

MALLORY DOLORFINO, LUKE MARTIN, ZACHARY SLONIM, YUXUAN SUN, YONG YANG

{"title":"ON THE CHARACTERISATION OF ALTERNATING GROUPS BY CODEGREES","authors":"MALLORY DOLORFINO, LUKE MARTIN, ZACHARY SLONIM, YUXUAN SUN, YONG YANG","doi":"10.1017/s0004972723001429","DOIUrl":"https://doi.org/10.1017/s0004972723001429","url":null,"abstract":"Let G be a finite group and $mathrm {Irr}(G)$ the set of all irreducible complex characters of G. Define the codegree of $chi in mathrm {Irr}(G)$ as $mathrm {cod}(chi ):={|G:mathrm {ker}(chi ) |}/{chi (1)}$ and let $mathrm {cod}(G):={mathrm {cod}(chi ) mid chi in mathrm {Irr}(G)}$ be the codegree set of G. Let $mathrm {A}_n$ be an alternating group of degree $n ge 5$ . We show that $mathrm {A}_n$ is determined up to isomorphism by $operatorname {cod}(mathrm {A}_n)$ .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"31 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139586153","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

COMPLETE EMBEDDINGS OF GROUPS 群的完全嵌入

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-26 DOI: 10.1017/s0004972723001442

MARTIN R. BRIDSON, HAMISH SHORT

{"title":"COMPLETE EMBEDDINGS OF GROUPS","authors":"MARTIN R. BRIDSON, HAMISH SHORT","doi":"10.1017/s0004972723001442","DOIUrl":"https://doi.org/10.1017/s0004972723001442","url":null,"abstract":"Every countable group G can be embedded in a finitely generated group $G^*$ that is hopfian and complete, that is, $G^*$ has trivial centre and every epimorphism $G^*to G^*$ is an inner automorphism. Every finite subgroup of $G^*$ is conjugate to a finite subgroup of G. If G has a finite presentation (respectively, a finite classifying space), then so does $G^*$ . Our construction of $G^*$ relies on the existence of closed hyperbolic 3-manifolds that are asymmetric and non-Haken.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"396 2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139586224","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

NEAR OPTIMAL THRESHOLDS FOR EXISTENCE OF DILATED CONFIGURATIONS IN 中存在扩张构型的近似最佳阈值

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-26 DOI: 10.1017/s0004972723001399

PABLO BHOWMIK, FIRDAVS RAKHMONOV

引用次数: 0

BOUNDING ZETA ON THE 1-LINE UNDER THE PARTIAL RIEMANN HYPOTHESIS 部分里曼假设下的单线上的Zeta界限

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-10 DOI: 10.1017/s0004972723001338

ANDRÉS CHIRRE

引用次数: 0

COUNTING UNIONS OF SCHREIER SETS 施赖尔集合的计数联合

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2023-12-27 DOI: 10.1017/s0004972723001326

KEVIN BEANLAND, DMITRIY GOROVOY, JĘDRZEJ HODOR, DANIIL HOMZA

{"title":"COUNTING UNIONS OF SCHREIER SETS","authors":"KEVIN BEANLAND, DMITRIY GOROVOY, JĘDRZEJ HODOR, DANIIL HOMZA","doi":"10.1017/s0004972723001326","DOIUrl":"https://doi.org/10.1017/s0004972723001326","url":null,"abstract":"A subset of positive integers F is a Schreier set if it is nonempty and $|F|leqslant min F$ (here $|F|$ is the cardinality of F). For each positive integer k, we define $kmathcal {S}$ as the collection of all the unions of at most k Schreier sets. Also, for each positive integer n, let $(kmathcal {S})^n$ be the collection of all sets in $kmathcal {S}$ with maximum element equal to n. It is well known that the sequence $(|(1mathcal {S})^n|)_{n=1}^infty $ is the Fibonacci sequence. In particular, the sequence satisfies a linear recurrence. We show that the sequence $(|(kmathcal {S})^n|)_{n=1}^infty $ satisfies a linear recurrence for every positive k.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"7 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139052831","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

SOLVABLE GROUPS WHOSE NONNORMAL SUBGROUPS HAVE FEW ORDERS 非正常子群阶数少的可解群

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2023-12-27 DOI: 10.1017/s0004972723001168

LIJUAN HE, HENG LV, GUIYUN CHEN

{"title":"SOLVABLE GROUPS WHOSE NONNORMAL SUBGROUPS HAVE FEW ORDERS","authors":"LIJUAN HE, HENG LV, GUIYUN CHEN","doi":"10.1017/s0004972723001168","DOIUrl":"https://doi.org/10.1017/s0004972723001168","url":null,"abstract":"Suppose that G is a finite solvable group. Let $t=n_c(G)$ denote the number of orders of nonnormal subgroups of G. We bound the derived length $dl(G)$ in terms of $n_c(G)$ . If G is a finite p-group, we show that $|G'|leq p^{2t+1}$ and $dl(G)leq lceil log _2(2t+3)rceil $ . If G is a finite solvable nonnilpotent group, we prove that the sum of the powers of the prime divisors of $|G'|$ is less than t and that $dl(G)leq lfloor 2(t+1)/3rfloor +1$ .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"109 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139052909","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

INTERSECTING THE TORSION OF ELLIPTIC CURVES 与椭圆曲线的扭转相交

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2023-12-27 DOI: 10.1017/s000497272300134x

NATALIA GARCIA-FRITZ, HECTOR PASTEN

{"title":"INTERSECTING THE TORSION OF ELLIPTIC CURVES","authors":"NATALIA GARCIA-FRITZ, HECTOR PASTEN","doi":"10.1017/s000497272300134x","DOIUrl":"https://doi.org/10.1017/s000497272300134x","url":null,"abstract":"Bogomolov and Tschinkel [‘Algebraic varieties over small fields’, <jats:italic>Diophantine Geometry</jats:italic>, U. Zannier (ed.), CRM Series, 4 (Scuola Normale Superiore di Pisa, Pisa, 2007), 73–91] proved that, given two complex elliptic curves <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S000497272300134X_inline1.png\" /> <jats:tex-math> $E_1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S000497272300134X_inline2.png\" /> <jats:tex-math> $E_2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> along with even degree-<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S000497272300134X_inline3.png\" /> <jats:tex-math> $2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> maps <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S000497272300134X_inline4.png\" /> <jats:tex-math> $pi _jcolon E_jto mathbb {P}^1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> having different branch loci, the intersection of the image of the torsion points of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S000497272300134X_inline5.png\" /> <jats:tex-math> $E_1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S000497272300134X_inline6.png\" /> <jats:tex-math> $E_2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> under their respective <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S000497272300134X_inline7.png\" /> <jats:tex-math> $pi _j$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is finite. They conjectured (also in works with Fu) that the cardinality of this intersection is uniformly bounded independently of the elliptic curves. The recent proof of the uniform Manin–Mumford conjecture implies a full solution of the Bogomolov–Fu–Tschinkel conjecture. In this paper, we prove a generalisation of the Bogomolov–Fu–Tschinkel conjecture whereby, instead of even degree-<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S000497272300134X_inline8.png\" /> <jats:tex-math> $2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> maps, one can use any rational functions of bounded degree on the elliptic curves as long as they have different branch loci. Our approach combines Nevanlinna th","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"30 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053000","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

DIVISIBILITY OF SUMS OF PARTITION NUMBERS BY MULTIPLES OF 2 AND 3 2 和 3 的倍数分割数之和的可分割性

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2023-12-22 DOI: 10.1017/s0004972723001351

Nayandeep Deka Baruah

{"title":"DIVISIBILITY OF SUMS OF PARTITION NUMBERS BY MULTIPLES OF 2 AND 3","authors":"Nayandeep Deka Baruah","doi":"10.1017/s0004972723001351","DOIUrl":"https://doi.org/10.1017/s0004972723001351","url":null,"abstract":"\u0000\t We show that certain sums of partition numbers are divisible by multiples of 2 and 3. For example, if \u0000\t \u0000\t\t\u0000\t\t\u0000$p(n)$\u0000\u0000\t \u0000\t denotes the number of unrestricted partitions of a positive integer n (and \u0000\t \u0000\t\t\u0000\t\t\u0000$p(0)=1$\u0000\u0000\t \u0000\t , \u0000\t \u0000\t\t\u0000\t\t\u0000$p(n)=0$\u0000\u0000\t \u0000\t for \u0000\t \u0000\t\t\u0000\t\t\u0000$n<0$\u0000\u0000\t \u0000\t ), then for all nonnegative integers m, \u0000\t \u0000\t\t\u0000\t\t\u0000$$ begin{align*}sum_{k=0}^infty p(24m+23-omega(-2k))+sum_{k=1}^infty p(24m+23-omega(2k))equiv 0~ (text{mod}~144),end{align*} $$\u0000\u0000\t \u0000\t \u0000\t where \u0000\t \u0000\t\t\u0000\t\t\u0000$omega (k)=k(3k+1)/2$\u0000\u0000\t \u0000\t .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"3 9","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138945112","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 NOTE ON THE ZEROS OF L-FUNCTIONS ASSOCIATED TO FIXED-ORDER DIRICHLET CHARACTERS 关于与定阶德里克特字符相关的 l 函数零点的注释

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2023-12-18 DOI: 10.1017/s0004972723001156

C. C. CORRIGAN

引用次数: 0