发布求助
文献互助 智能选刊 最新文献

Algebra and Logic最新文献

筛选
英文 中文
Toward a Sharp Baer–Suzuki Theorem for the π-Radical: Exceptional Groups of Small Rank 迈向π-激进的巴尔-铃木锐定理：小等级的特殊群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-01-04 DOI: 10.1007/s10469-023-09720-3
Zh. Wang, W. Guo, D. O. Revin
{"title":"Toward a Sharp Baer–Suzuki Theorem for the π-Radical: Exceptional Groups of Small Rank","authors":"Zh. Wang,&nbsp;W. Guo,&nbsp;D. O. Revin","doi":"10.1007/s10469-023-09720-3","DOIUrl":"10.1007/s10469-023-09720-3","url":null,"abstract":"<p>Let π be a proper subset of the set of all prime numbers. Denote by <i>r</i> the least prime number not in π, and put <i>m</i> = <i>r</i>, if <i>r</i> = 2, 3, and m = <i>r</i> − 1 if <i>r</i> ≥ 5. We look at the conjecture that a conjugacy class <i>D</i> in a finite group <i>G</i> generates a π-subgroup in <i>G</i> (or, equivalently, is contained in the π-radical) iff any m elements from <i>D</i> generate a π-group. Previously, this conjecture was confirmed for finite groups whose every non-Abelian composition factor is isomorphic to a sporadic, alternating, linear or unitary simple group. Now it is confirmed for groups the list of composition factors of which is added up by exceptional groups of Lie type <sup>2</sup><i>B</i><sub>2</sub>(<i>q</i>), <sup>2</sup><i>G</i><sub>2</sub>(<i>q</i>), <i>G</i><sub>2</sub>(<i>q</i>), and <sup>3</sup><i>D</i><sub>4</sub>(<i>q</i>).</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"1 - 21"},"PeriodicalIF":0.4,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Finite Groups with a Soluble Group of Coprime Automorphisms Whose Fixed Points Have Bounded Engel Sinks 定点具有有界恩格尔下沉的可溶同素自动形群有限群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-01-04 DOI: 10.1007/s10469-023-09727-w
E. I. Khukhro, P. Shumyatsky
{"title":"Finite Groups with a Soluble Group of Coprime Automorphisms Whose Fixed Points Have Bounded Engel Sinks","authors":"E. I. Khukhro,&nbsp;P. Shumyatsky","doi":"10.1007/s10469-023-09727-w","DOIUrl":"10.1007/s10469-023-09727-w","url":null,"abstract":"<p>Suppose that a finite group <i>G</i> admits a soluble group of coprime automorphisms A. We prove that if, for some positive integer <i>m</i>, every element of the centralizer <i>C</i><sub><i>G</i></sub>(<i>A</i>) has a left Engel sink of cardinality at most <i>m</i> (or a right Engel sink of cardinality at most <i>m</i>), then <i>G</i> has a subgroup of (|<i>A</i>|,<i>m</i>)-bounded index which has Fitting height at most 2α(<i>A</i>) + 2, where α(<i>A</i>) is the composition length of <i>A</i>. We also prove that if, for some positive integer <i>r</i>, every element of the centralizer <i>C</i><sub><i>G</i></sub>(<i>A</i>) has a left Engel sink of rank at most <i>r</i> (or a right Engel sink of rank at most <i>r</i>), then <i>G</i> has a subgroup of (|<i>A</i>|, <i>r</i>)-bounded index which has Fitting height at most 4α(A) + 4α(A) + 3. Here, a left Engel sink of an element g of a group <i>G</i> is a set <i>𝔈</i> (<i>g</i>) such that for every <i>x</i> ∈ <i>G</i> all sufficiently long commutators [...[[<i>x</i>, <i>g</i>], <i>g</i>], . . . , <i>g</i>] belong to <i>𝔈</i> (<i>g</i>). (Thus, g is a left Engel element precisely when we can choose (g) = {1}.) A right Engel sink of an element g of a group <i>G</i> is a set <i>ℜ</i>(<i>g</i>) such that for every <i>x</i> ∈ <i>G</i> all sufficiently long commutators [...[[g, x], x], . . . , x] belong to <i>ℜ</i>(<i>g</i>). Thus, <i>g</i> is a right Engel element precisely when we can choose <i>ℜ</i>(<i>g</i>) = {1}.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"80 - 93"},"PeriodicalIF":0.4,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Primitive Prime Divisors of Orders of Suzuki–Ree Groups 铃木李群阶的原始素除数
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-01-03 DOI: 10.1007/s10469-023-09722-1
M. A. Grechkoseeva
{"title":"Primitive Prime Divisors of Orders of Suzuki–Ree Groups","authors":"M. A. Grechkoseeva","doi":"10.1007/s10469-023-09722-1","DOIUrl":"10.1007/s10469-023-09722-1","url":null,"abstract":"<p>There is a well-known factorization of the number 2<sup>2<i>m</i></sup> + 1<i>,</i> with m odd, related to the orders of tori of simple Suzuki groups: 2<sup>2<i>m</i></sup> +1 is a product of <i>a</i> = 2<sup><i>m</i></sup> + 2<sup>(<i>m</i>+1)<i>/</i>2</sup> +1 and <i>b</i> = 2<sup><i>m</i></sup><i> −</i> 2<sup>(<i>m</i>+1)<i>/</i>2</sup> + 1. By the Bang–Zsigmondy theorem, there is a primitive prime divisor of 2<sup>4<i>m</i></sup><i> −</i> 1, that is, a prime r that divides 2<sup>4<i>m</i></sup> − 1 and does not divide 2<sup><i>i</i></sup><i> −</i> 1 for any 1 ≤ <i>i &lt;</i> 4<i>m.</i> It is easy to see that r divides 2<sup>2<i>m</i></sup> + 1, and so it divides one of the numbers <i>a</i> and <i>b.</i> It is proved that for every <i>m &gt;</i> 5, each of <i>a, b</i> is divisible by some primitive prime divisor of 2<sup>4<i>m</i></sup><i> −</i> 1. Similar results are obtained for primitive prime divisors related to the simple Ree groups. As an application, we find the independence and 2-independence numbers of the prime graphs of almost simple Suzuki–Ree groups.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"41 - 49"},"PeriodicalIF":0.4,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139096709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Generic Types and Generic Elements in Divisible Rigid Groups 可分刚性群中的通用类型和通用元素
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-01-03 DOI: 10.1007/s10469-023-09726-x
A. G. Myasnikov, N. S. Romanovskii
{"title":"Generic Types and Generic Elements in Divisible Rigid Groups","authors":"A. G. Myasnikov,&nbsp;N. S. Romanovskii","doi":"10.1007/s10469-023-09726-x","DOIUrl":"10.1007/s10469-023-09726-x","url":null,"abstract":"<p>A group <i>G</i> is said to be m-rigid if it contains a normal series of the form <i>G</i> = <i>G</i><sub>1</sub> &gt; <i>G</i><sub>2</sub> &gt; . . . &gt; <i>G</i><sub><i>m</i></sub> &gt; <i>G</i><sub><i>m+</i>1</sub> = 1, whose quotients <i>G</i><sub><i>i</i></sub>/<i>G</i><sub><i>i+</i>1</sub> are Abelian and, treated as (right) ℤ[<i>G</i>/<i>G</i><sub><i>i</i></sub>]-modules, are torsion-free. A rigid group <i>G</i> is said to be divisible if elements of the quotient <i>ρ</i><sub><i>i</i></sub>(<i>G</i>)/<i>ρ</i><sub><i>i+</i>1</sub>(<i>G</i>) are divisible by nonzero elements of the ring ℤ[<i>G</i>/<i>ρ</i><sub><i>i</i></sub>(<i>G</i>)]. Previously, it was proved that the theory of divisible m-rigid groups is complete and ω-stable. In the present paper, we give an algebraic description of elements and types that are generic over a divisible m-rigid group <i>G</i>.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"72 - 79"},"PeriodicalIF":0.4,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139096549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Finite 4-Primary Groups with Disconnected Gruenberg–Kegel Graph Containing a Triangle 包含三角形的断开格伦伯格-凯格尔图的有限四元组
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-01-03 DOI: 10.1007/s10469-023-09724-z
A. S. Kondrat’ev
{"title":"Finite 4-Primary Groups with Disconnected Gruenberg–Kegel Graph Containing a Triangle","authors":"A. S. Kondrat’ev","doi":"10.1007/s10469-023-09724-z","DOIUrl":"10.1007/s10469-023-09724-z","url":null,"abstract":"<p>We give a description of finite 4-primary groups with disconnected Gruenberg–Kegel graph containing a triangle. As a corollary, finite groups whose Gruenberg–Kegel graph coincides with the Gruenberg–Kegel graph of <sup>3</sup>D<sub>4</sub>(2) are exemplified, which generalizes V. D. Mazurov’ description of finite groups isospectral to the group <sup>3</sup>D<sub>4</sub>(2).</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"54 - 65"},"PeriodicalIF":0.4,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 p-Index Extremal Groups 关于 p 指数极值群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-01-03 DOI: 10.1007/s10469-023-09728-9
A. V. Vasil’ev, I. B. Gorshkov
{"title":"On p-Index Extremal Groups","authors":"A. V. Vasil’ev,&nbsp;I. B. Gorshkov","doi":"10.1007/s10469-023-09728-9","DOIUrl":"10.1007/s10469-023-09728-9","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"94 - 99"},"PeriodicalIF":0.4,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Shunkov Groups Saturated with Almost Simple Groups 几乎简单群饱和的 Shunkov 群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-12-28 DOI: 10.1007/s10469-023-09725-y
N. V. Maslova, A. A. Shlepkin
{"title":"Shunkov Groups Saturated with Almost Simple Groups","authors":"N. V. Maslova,&nbsp;A. A. Shlepkin","doi":"10.1007/s10469-023-09725-y","DOIUrl":"10.1007/s10469-023-09725-y","url":null,"abstract":"<p>A group <i>G</i> is called a Shunkov group (a conjugate biprimitive finite group) if, for any of its finite subgroups <i>H</i> in the factor group <i>N</i><sub><i>G</i></sub>(<i>H</i>)/<i>H</i>, every two conjugate elements of prime order generate a finite subgroup. We say that a group is saturated with groups from the set 𝔐 if any finite subgroup of the given group is contained in its subgroup isomorphic to some group in 𝔐. We show that a Shunkov group <i>G</i> which is saturated with groups from the set 𝔐 possessing specific properties, and contains an involution <i>z</i> with the property that the centralizer <i>C</i><sub><i>G</i></sub>(<i>z</i>) has only finitely many elements of finite order will have a periodic part isomorphic to one of the groups in 𝔐. In particular, a Shunkov group <i>G</i> that is saturated with finite almost simple groups and contains an involution <i>z</i> with the property that the centralizer <i>C</i><sub><i>G</i></sub>(<i>z</i>) has only finitely many elements of finite order will have a periodic part isomorphic to a finite almost simple group.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"66 - 71"},"PeriodicalIF":0.4,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139064294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Unsolvability of Finite Groups Isospectral to the Automorphism Group of the Second Sporadic Janko Group 与第二时空扬科群的自变群同谱的有限群的不可解性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-12-28 DOI: 10.1007/s10469-023-09723-0
A. Kh. Zhurtov, D. V. Lytkina, V. D. Mazurov
{"title":"Unsolvability of Finite Groups Isospectral to the Automorphism Group of the Second Sporadic Janko Group","authors":"A. Kh. Zhurtov,&nbsp;D. V. Lytkina,&nbsp;V. D. Mazurov","doi":"10.1007/s10469-023-09723-0","DOIUrl":"10.1007/s10469-023-09723-0","url":null,"abstract":"<p>For a finite group G, the spectrum is the set ω(G) of element orders of the group G. The spectrum of G is closed under divisibility and is therefore uniquely determined by the set μ(G) consisting of elements of ω(G) that are maximal with respect to divisibility. We prove that a finite group isospectral to Aut(J<sub>2</sub>) is unsolvable.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"50 - 53"},"PeriodicalIF":0.4,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139064341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Sessions of the Seminar “Algebra i Logika” 代数与逻辑 "研讨会课程
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-12-16 DOI: 10.1007/s10469-023-09729-8
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-023-09729-8","DOIUrl":"10.1007/s10469-023-09729-8","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 1","pages":"100 - 101"},"PeriodicalIF":0.4,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Families of Permutations and Ideals of Turing Degrees 排列族与图灵度理想
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-12-04 DOI: 10.1007/s10469-023-09714-1
A. S. Morozov, V. G. Puzarenko, M. Kh. Faizrachmanov
{"title":"Families of Permutations and Ideals of Turing Degrees","authors":"A. S. Morozov,&nbsp;V. G. Puzarenko,&nbsp;M. Kh. Faizrachmanov","doi":"10.1007/s10469-023-09714-1","DOIUrl":"10.1007/s10469-023-09714-1","url":null,"abstract":"<p>Families 𝒫<sub>I</sub> consisting of permutations of the natural numbers ω whose degrees belong to an ideal I of Turing degrees, as well as their jumps <span>({mathcal{P}}_{mathrm{I}}{prime})</span>, are studied. For any countable Turing ideal I, the degree spectra of families 𝒫<sub>I</sub> and their jumps <span>({mathcal{P}}_{mathrm{I}}{prime})</span> are described. For some ideals I generated by c.e. degrees, the spectra of families 𝒫<sub>I</sub> are defined.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 6","pages":"481 - 490"},"PeriodicalIF":0.4,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138529801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信