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International Journal of Group Theory最新文献

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Groups with numerical restrictions on minimal generating sets 极小生成集上具有数值限制的群
IF 0.2
International Journal of Group Theory Pub Date : 2019-02-01 DOI: 10.22108/IJGT.2019.115131.1526
L. A. Kurdachenko, P. Longobardi, M. Maj
{"title":"Groups with numerical restrictions on minimal generating sets","authors":"L. A. Kurdachenko, P. Longobardi, M. Maj","doi":"10.22108/IJGT.2019.115131.1526","DOIUrl":"https://doi.org/10.22108/IJGT.2019.115131.1526","url":null,"abstract":"We study an inverse problem of small doubling type. We investigate the structure of a finitely generated group $G$ such that, for any set $S$ of generators of $G$ of minimal order, we have $S^2 leq 3|S|-beta$, where $beta in {1, 2, 3}$","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43007003","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: 2
On noninner automorphisms of finite $p$-groups that fix the center elementwise 中心固定的有限p群的非内自同构
IF 0.2
International Journal of Group Theory Pub Date : 2019-01-13 DOI: 10.22108/IJGT.2018.108082.1457
S. Ghoraishi
{"title":"On noninner automorphisms of finite $p$-groups that fix the center elementwise","authors":"S. Ghoraishi","doi":"10.22108/IJGT.2018.108082.1457","DOIUrl":"https://doi.org/10.22108/IJGT.2018.108082.1457","url":null,"abstract":"In this paper we show that every finite nonabelian $p$-group $G$ in which the Frattini subgroup $Phi(G)$ has order $leq p^5$ admits a noninner automorphism of order $p$ leaving the center $Z(G)$ elementwise fixed. As a consequence it follows that the order of a possible counterexample to the conjecture of Berkovich is at least $p^8$.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2019-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43953016","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: 1
On some generalization of the malnormal subgroups 关于非正规子群的一些推广
IF 0.2
International Journal of Group Theory Pub Date : 2018-12-09 DOI: 10.22108/ijgt.2018.112124.1487
I. Subbotin, L. A. Kurdachenko, N. N. Semko
{"title":"On some generalization of the malnormal subgroups","authors":"I. Subbotin, L. A. Kurdachenko, N. N. Semko","doi":"10.22108/ijgt.2018.112124.1487","DOIUrl":"https://doi.org/10.22108/ijgt.2018.112124.1487","url":null,"abstract":"A subgroup H of a group G is called malonormal in G if H ∩H = ⟨1⟩ for every element x / ∈ NG(H). These subgroups are generalizations of malnormal subgroups. Every malnormal subgroup is malonormal, and every selfnormalizing malonormal subgroup is malnormal. Furthermore, every normal subgroup is malonormal. In this paper we obtain a description of finite and certain infinite groups, whose subgroups are malonormal.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2018-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42675004","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: 0
$4$-quasinormal subgroups of prime order $4$-素阶的拟正规子群
IF 0.2
International Journal of Group Theory Pub Date : 2018-12-09 DOI: 10.22108/IJGT.2018.113482.1510
S. Stonehewer
{"title":"$4$-quasinormal subgroups of prime order","authors":"S. Stonehewer","doi":"10.22108/IJGT.2018.113482.1510","DOIUrl":"https://doi.org/10.22108/IJGT.2018.113482.1510","url":null,"abstract":"‎Generalizing the concept of quasinormality‎, ‎a subgroup $H$ of a group $G$ is said to be 4-quasinormal in $G$ if‎, ‎for all cyclic subgroups $K$ of $G$‎, ‎$langle H,Krangle=HKHK$‎. ‎An intermediate concept would be 3-quasinormality‎, ‎but in finite $p$-groups‎ - ‎our main concern‎ - ‎this is equivalent to quasinormality‎. ‎Quasinormal subgroups have many interesting properties and it has been shown that some of them can be extended to 4-quasinormal subgroups‎, ‎particularly in finite‎ ‎$p$-groups‎. ‎However‎, ‎even in the smallest case‎, ‎when $H$ is a 4-quasinormal subgroup of order $p$ in a finite $p$-group $G$‎, ‎precisely how $H$ is embedded in $G$‎ ‎is not immediately obvious‎. ‎Here we consider one of these questions regarding the commutator subgroup $[H,G]$‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2018-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48755768","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: 1
On embedding of partially commutative metabelian groups to matrix groups 部分可交换亚元群与矩阵群的嵌入
IF 0.2
International Journal of Group Theory Pub Date : 2018-12-01 DOI: 10.22108/IJGT.2017.21478
E. Timoshenko
{"title":"On embedding of partially commutative metabelian groups to matrix groups","authors":"E. Timoshenko","doi":"10.22108/IJGT.2017.21478","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21478","url":null,"abstract":"‎The Magnus embedding of a free metabelian group induces the embedding of partially commutative metabelian group $S_Gamma$ in a group of matrices $M_Gamma$. Properties and the universal theory of the group $M_Gamma$ are studied.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43043454","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: 2
On nonsolvable groups whose prime degree graphs have four vertices and one triangle 素度图有四个顶点和一个三角形的不可解群
IF 0.2
International Journal of Group Theory Pub Date : 2018-09-01 DOI: 10.22108/IJGT.2017.21476
R. Hafezieh
{"title":"On nonsolvable groups whose prime degree graphs have four vertices and one triangle","authors":"R. Hafezieh","doi":"10.22108/IJGT.2017.21476","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21476","url":null,"abstract":"‎Let $G$ be a finite group‎. ‎The prime degree graph of $G$‎, ‎denoted‎ ‎by $Delta(G)$‎, ‎is an undirected graph whose vertex set is $rho(G)$ and there is an edge‎ ‎between two distinct primes $p$ and $q$ if and only if $pq$ divides some irreducible‎ ‎character degree of $G$‎. ‎In general‎, ‎it seems that the prime graphs‎ ‎contain many edges and thus they should have many triangles‎, ‎so one of the cases that would be interesting is to consider those finite groups whose prime degree graphs have a small number of triangles‎. ‎In this paper we consider the case where for a nonsolvable group $G$‎, ‎$Delta(G)$ is a connected graph which has only one triangle and four vertices‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47541235","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: 1
On some integral representations of groups and global irreducibility. 关于群的一些积分表示和全局不可约性。
IF 0.2
International Journal of Group Theory Pub Date : 2018-09-01 DOI: 10.22108/IJGT.2017.100688.1402
D. Malinin
{"title":"On some integral representations of groups and global irreducibility.","authors":"D. Malinin","doi":"10.22108/IJGT.2017.100688.1402","DOIUrl":"https://doi.org/10.22108/IJGT.2017.100688.1402","url":null,"abstract":"Arithmetic aspects of integral representations of finite groups and their irreducibility are considered with a focus on globally irreducible representations and their generalizations to arithmetic rings. Certain problems concerning integral irreducible two-dimensional representations over number rings are discussed. Let $K$ be a \u001cfinite extension of the rational number \u001cfield and $O_K$ the ring of integers of $K$. Let $G$ be a \u001cfinite subgroup of $GL(2,K)$, the group of $(2 times 2)$-matrices over $K$. We obtain some conditions on $K$ for $G$ to be conjugate to a subgroup of $GL(2,O_K)$.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47608354","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: 0
Fragile words and Cayley type transducers 脆弱词与Cayley型换能器
IF 0.2
International Journal of Group Theory Pub Date : 2018-09-01 DOI: 10.22108/IJGT.2017.100358.1398
D. D’Angeli, E. Rodaro
{"title":"Fragile words and Cayley type transducers","authors":"D. D’Angeli, E. Rodaro","doi":"10.22108/IJGT.2017.100358.1398","DOIUrl":"https://doi.org/10.22108/IJGT.2017.100358.1398","url":null,"abstract":"We address the problem of finding examples of non-bireversible transducers defining free groups, we show examples of transducers with sink accessible from every state which generate free groups, and, in general, we link this problem to the non-existence of certain words with interesting combinatorial and geometrical properties that we call fragile words. By using this notion, we exhibit a series of transducers constructed from Cayley graphs of finite groups whose defined semigroups are free, and thus having exponential growth.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47137389","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: 0
Groups with permutability conditions for subgroups of infinite rank 无限秩子群的可置换条件群
IF 0.2
International Journal of Group Theory Pub Date : 2018-09-01 DOI: 10.22108/IJGT.2017.21483
A. V. D. Luca, R. Ialenti
{"title":"Groups with permutability conditions for subgroups of infinite rank","authors":"A. V. D. Luca, R. Ialenti","doi":"10.22108/IJGT.2017.21483","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21483","url":null,"abstract":"In this paper, the structure of non-periodic generalized radical groups of infinite rank whose subgroups of infinite rank satisfy a suitable permutability condition is investigated.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45754082","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: 1
Graham Higman's PORC theorem Graham Higman的PORC定理
IF 0.2
International Journal of Group Theory Pub Date : 2018-08-13 DOI: 10.22108/IJGT.2018.112574.1498
M. Vaughan-Lee
{"title":"Graham Higman's PORC theorem","authors":"M. Vaughan-Lee","doi":"10.22108/IJGT.2018.112574.1498","DOIUrl":"https://doi.org/10.22108/IJGT.2018.112574.1498","url":null,"abstract":"Graham Higman published two important papers in 1960‎. ‎In the first of these‎ ‎papers he proved that for any positive integer $n$ the number of groups of‎ ‎order $p^{n}$ is bounded by a polynomial in $p$‎, ‎and he formulated his famous‎ ‎PORC conjecture about the form of the function $f(p^{n})$ giving the number of‎ ‎groups of order $p^{n}$‎. ‎In the second of these two papers he proved that the‎ ‎function giving the number of $p$-class two groups of order $p^{n}$ is PORC‎. ‎He established this result as a corollary to a very general result about‎ ‎vector spaces acted on by the general linear group‎. ‎This theorem takes over a‎ ‎page to state‎, ‎and is so general that it is hard to see what is going on‎. ‎Higman's proof of this general theorem contains several new ideas and is quite‎ ‎hard to follow‎. ‎However in the last few years several authors have developed‎ ‎and implemented algorithms for computing Higman's PORC formulae in‎ ‎special cases of his general theorem‎. ‎These algorithms give perspective on‎ ‎what are the key points in Higman's proof‎, ‎and also simplify parts of the proof‎. ‎In this note I give a proof of Higman's general theorem written in the light‎ ‎of these recent developments‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2018-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45248140","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: 3
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