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Uncountable groups with finitely many normalizers of large subgroups 具有有限多个正常化大子群的不可数群
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-18 DOI: 10.1007/s00013-023-01953-z
M. De Falco, C. Musella, G. Sabatino
{"title":"Uncountable groups with finitely many normalizers of large subgroups","authors":"M. De Falco, C. Musella, G. Sabatino","doi":"10.1007/s00013-023-01953-z","DOIUrl":"https://doi.org/10.1007/s00013-023-01953-z","url":null,"abstract":"<p>In this paper, the structure of uncountable groups with finitely many normalizers of large subgroups is studied and the connections between this property and other natural finiteness conditions on large subgroups of uncountable groups are investigated. In particular, groups in which every large subgroup is close to be normal with the only obstruction of a finite section and groups with finitely many commutator subgroups of large subgroups are considered. Moreover, groups with a finite covering consisting of groups with normal large subgroups are studied.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139497997","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 short proof of the elliptical range theorem 椭圆范围定理的简短证明
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-17 DOI: 10.1007/s00013-023-01957-9
Gyula Lakos
{"title":"A short proof of the elliptical range theorem","authors":"Gyula Lakos","doi":"10.1007/s00013-023-01957-9","DOIUrl":"https://doi.org/10.1007/s00013-023-01957-9","url":null,"abstract":"<p>A short proof of the elliptical range theorem concerning the numerical range of <span>(2times 2)</span> complex matrices is given.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139498061","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 slope stability of the cotangent bundles of Weierstrass fibrations 论魏尔斯特拉斯纤维余切束的斜率稳定性
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-17 DOI: 10.1007/s00013-023-01958-8
Valentin Boboc
{"title":"On the slope stability of the cotangent bundles of Weierstrass fibrations","authors":"Valentin Boboc","doi":"10.1007/s00013-023-01958-8","DOIUrl":"https://doi.org/10.1007/s00013-023-01958-8","url":null,"abstract":"<p>We provide a full classification of the slope stability of the cotangent bundles of relatively minimal smooth Weierstrass fibrations. The classification only depends on the topological Euler characteristic of the surface and the genus of the base curve.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139497953","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
Tame symmetric algebras of period four 周期为四的驯服对称代数
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-17 DOI: 10.1007/s00013-023-01954-y
Karin Erdmann, Adam Hajduk, Adam Skowyrski
{"title":"Tame symmetric algebras of period four","authors":"Karin Erdmann, Adam Hajduk, Adam Skowyrski","doi":"10.1007/s00013-023-01954-y","DOIUrl":"https://doi.org/10.1007/s00013-023-01954-y","url":null,"abstract":"<p>In this paper, we are concerned with the structure of tame symmetric algebras <span>(Lambda )</span> of period four (TSP4 algebras for short). For a tame algebra, the number of arrows starting or ending at a given vertex cannot be large. Here we will mostly focus on the case when the Gabriel quiver of <span>(Lambda )</span> is biserial, that is, there are at most two arrows ending and at most two arrows starting at each vertex. We present a range of properties (with relatively short proofs) which must hold for the Gabriel quiver of such an algebra. In particular, we show that triangles (and squares) appear naturally, so as for weighted surface algebras (Erdmann and Skowroński in J Algebra 505:490–558, 2018, J Algebra 544:170–227, 2020, J Algebra 569:875–889, 2021). Furthermore, we prove results on the minimal relations defining the ideal <i>I</i> for an admissible presentation of <span>(Lambda )</span> in the form <i>KQ</i>/<i>I</i>. This will be the input for the classification of all TSP4 algebras with biserial Gabriel quiver.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139498060","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
Monogenity of iterates of polynomials 多项式迭代的同源性
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-16 DOI: 10.1007/s00013-023-01949-9
{"title":"Monogenity of iterates of polynomials","authors":"","doi":"10.1007/s00013-023-01949-9","DOIUrl":"https://doi.org/10.1007/s00013-023-01949-9","url":null,"abstract":"<h3>Abstract</h3> <p>In this article, we study the monogenity of a tower of number fields defined by the iterates of a stable polynomial. We give a necessary condition for the monogenity of the number fields defined by the iterates of a stable polynomial. When the stable polynomial is of certain type, we also give a sufficient condition for the monogenity of the fields defined by each of its iterate. As a consequence, we obtain an infinite 3-tower of monogenic number fields. Moreover, we construct an infinite family of stable polynomials such that each of its iterate is non-monogenic.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139475341","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
Weight $$mathbf {1/2}$$ multiplier systems for the group $$mathbf {Gamma _0^+({varvec{p}})}$$ and a geometric formulation 组 $$mathbf {1/2}$ 的权 $$mathbf {Gamma _0^+({varvec{p}})}$ 乘法系统和几何公式
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-16 DOI: 10.1007/s00013-023-01948-w
{"title":"Weight $$mathbf {1/2}$$ multiplier systems for the group $$mathbf {Gamma _0^+({varvec{p}})}$$ and a geometric formulation","authors":"","doi":"10.1007/s00013-023-01948-w","DOIUrl":"https://doi.org/10.1007/s00013-023-01948-w","url":null,"abstract":"<h3>Abstract</h3> <p>We construct a weight 1/2 multiplier system for the group <span> <span>(Gamma _0^+(p))</span> </span>, the normalizer of the congruence subgroup <span> <span>(Gamma _0(p))</span> </span> where <em>p</em> is an odd prime, and we define an analogue of the eta function and Rademacher symbol and relate it to the geometry of edge paths in a triangulation of the upper half-plane.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139497998","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 conciseness of the word in Olshanskii’s example 关于奥尔尚斯基所举例子中词语的简洁性
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-13 DOI: 10.1007/s00013-023-01955-x
{"title":"On conciseness of the word in Olshanskii’s example","authors":"","doi":"10.1007/s00013-023-01955-x","DOIUrl":"https://doi.org/10.1007/s00013-023-01955-x","url":null,"abstract":"<h3>Abstract</h3> <p>A group-word <em>w</em> is called concise if the verbal subgroup <em>w</em>(<em>G</em>) is finite whenever <em>w</em> takes only finitely many values in a group <em>G</em>. It is known that there are words that are not concise. In particular, Olshanskii gave an example of such a word, which we denote by <span> <span>(w_o)</span> </span>. The problem whether every word is concise in the class of residually finite groups remains wide open. In this note, we observe that <span> <span>(w_o)</span> </span> is concise in residually finite groups. Moreover, we show that <span> <span>(w_o)</span> </span> is strongly concise in profinite groups, that is, <span> <span>(w_o(G))</span> </span> is finite whenever <em>G</em> is a profinite group in which <span> <span>(w_o)</span> </span> takes less than <span> <span>(2^{aleph _0})</span> </span> values.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139462025","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
$$L_p$$ Blaschke–Santaló and Petty projection inequalities in Gaussian space 高斯空间中的 $L_p$$ Blaschke-Santaló 和 Petty 投影不等式
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-12 DOI: 10.1007/s00013-023-01959-7
Junjie Shan, Wenxue Xu, Leiqin Yin
{"title":"$$L_p$$ Blaschke–Santaló and Petty projection inequalities in Gaussian space","authors":"Junjie Shan, Wenxue Xu, Leiqin Yin","doi":"10.1007/s00013-023-01959-7","DOIUrl":"https://doi.org/10.1007/s00013-023-01959-7","url":null,"abstract":"<p>The analogues of the <span>(L_p)</span> mixed volumes inequality, the <span>(L_p)</span> Brunn–Minkowski inequality, the <span>(L_p)</span> Blaschke–Santaló inequality, and the <span>(L_p)</span> Petty projection inequality in Gaussian space are established.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139462128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Partition of quadratic residues and non-residues in $$mathbb {Z}_p^*$$ for an odd prime p 奇素数 p 时 $$mathbb {Z}_p^*$ 中二次残差与非残差的划分
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-12 DOI: 10.1007/s00013-023-01942-2
Yathirajsharma M.V., Manjunatha M.R.
{"title":"Partition of quadratic residues and non-residues in $$mathbb {Z}_p^*$$ for an odd prime p","authors":"Yathirajsharma M.V., Manjunatha M.R.","doi":"10.1007/s00013-023-01942-2","DOIUrl":"https://doi.org/10.1007/s00013-023-01942-2","url":null,"abstract":"<p>Let <i>p</i> be an odd prime. In this article, we investigate the number of ways in which a quadratic residue and a non-residue modulo <i>p</i> can be expressed as sum of two quadratic residues sum of two quadratic non-residues, and sum of a quadratic residue and non-residue in an elementary way using Gauss sums.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139462158","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
Characters of prime power degree in principal blocks 主块中的素幂级数字符
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-01-03 DOI: 10.1007/s00013-023-01951-1
{"title":"Characters of prime power degree in principal blocks","authors":"","doi":"10.1007/s00013-023-01951-1","DOIUrl":"https://doi.org/10.1007/s00013-023-01951-1","url":null,"abstract":"<h3>Abstract</h3> <p>We describe finite groups whose principal block contains only characters of prime power degree.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139105271","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
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