Pub Date : 2018-06-25DOI: 10.22108/IJGT.2019.115366.1531
Nick Gill, Sam Hughes
In this paper we calculate the character table of a sharply $5$-transitive subgroup of ${rm Alt}(12)$, and of a sharply $4$-transitive subgroup of ${rm Alt}(11)$. Our presentation of these calculations is new because we make no reference to the sporadic simple Mathieu groups, and instead deduce the desired character tables using only the existence of the stated multiply transitive permutation representations.
{"title":"The character table of a sharply 5-transitive subgroup of the alternating group of degree 12","authors":"Nick Gill, Sam Hughes","doi":"10.22108/IJGT.2019.115366.1531","DOIUrl":"https://doi.org/10.22108/IJGT.2019.115366.1531","url":null,"abstract":"In this paper we calculate the character table of a sharply $5$-transitive subgroup of ${rm Alt}(12)$, and of a sharply $4$-transitive subgroup of ${rm Alt}(11)$. Our presentation of these calculations is new because we make no reference to the sporadic simple Mathieu groups, and instead deduce the desired character tables using only the existence of the stated multiply transitive permutation representations.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42935526","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}
Pub Date : 2018-06-01DOI: 10.22108/IJGT.2017.21480
A. Ballester-Bolinches
The aim of this survey article is to present some structural results about of groups whose Sylow p-subgroups are metacylic (p a prime). A complete characterisation of non-nilpotent groups whose 2-generator subgroups are metacyclic is also presented.
{"title":"On metacyclic subgroups of finite groups","authors":"A. Ballester-Bolinches","doi":"10.22108/IJGT.2017.21480","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21480","url":null,"abstract":"The aim of this survey article is to present some structural results about of groups whose Sylow p-subgroups are metacylic (p a prime). A complete characterisation of non-nilpotent groups whose 2-generator subgroups are metacyclic is also presented.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"7 1","pages":"25-29"},"PeriodicalIF":0.2,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48916110","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}
Pub Date : 2018-06-01DOI: 10.22108/IJGT.2017.21214
R. Esteban-Romero, G. Vincenzi
The research of the first author has been supported by the research grant MTM2014-54707-C3-1-P by the Ministerio de Economia y Competitividad (Spain) and FEDER (European Union).
{"title":"Some characterisations of groups in which normality is a transitive relation by means of subgroup embedding properties","authors":"R. Esteban-Romero, G. Vincenzi","doi":"10.22108/IJGT.2017.21214","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21214","url":null,"abstract":"The research of the first author has been supported by the research grant MTM2014-54707-C3-1-P by the Ministerio de Economia y Competitividad (Spain) and FEDER (European Union).","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"7 1","pages":"9-16"},"PeriodicalIF":0.2,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41470295","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}
Pub Date : 2018-06-01DOI: 10.22108/IJGT.2017.21475
M. J. Felipe, A. Martínez-Pastor, V. Ortiz-Sotomayor
The first author is supported by Proyecto Prometeo II/2015/011, and the third author acknowledges the doctorate scholarship “Ayudas para la contratacion de personal investigador en formacion de caracter predoctoral" granted by Generalitat Valenciana, Spain.
{"title":"On finite groups with square-free conjugacy class sizes","authors":"M. J. Felipe, A. Martínez-Pastor, V. Ortiz-Sotomayor","doi":"10.22108/IJGT.2017.21475","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21475","url":null,"abstract":"The first author is supported by Proyecto Prometeo II/2015/011, and the third author acknowledges the doctorate scholarship “Ayudas para la contratacion de personal investigador en formacion de caracter predoctoral\" granted by Generalitat Valenciana, Spain.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"7 1","pages":"17-24"},"PeriodicalIF":0.2,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41530331","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}
Pub Date : 2018-03-01DOI: 10.22108/IJGT.2017.21220
A. Lucchini
{"title":"Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements","authors":"A. Lucchini","doi":"10.22108/IJGT.2017.21220","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21220","url":null,"abstract":"","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"7 1","pages":"17-21"},"PeriodicalIF":0.2,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44769540","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}
Pub Date : 2018-03-01DOI: 10.22108/IJGT.2016.21218
S. Siani
The structure of groups which have at most two isomorphism classes of central factors ($B_2$-groups) are investigated. A complete description of $B_2$-groups is obtained in the locally finite case and in the nilpotent case. In addition detailed information is obtained about soluble $B_2$-groups. Also structural information about insoluble $B_2$-groups is given, in particular when such a group has the derived subgroup satisfying the minimal condition.
{"title":"On groups with two isomorphism classes of central factors","authors":"S. Siani","doi":"10.22108/IJGT.2016.21218","DOIUrl":"https://doi.org/10.22108/IJGT.2016.21218","url":null,"abstract":"The structure of groups which have at most two isomorphism classes of central factors ($B_2$-groups) are investigated. A complete description of $B_2$-groups is obtained in the locally finite case and in the nilpotent case. In addition detailed information is obtained about soluble $B_2$-groups. Also structural information about insoluble $B_2$-groups is given, in particular when such a group has the derived subgroup satisfying the minimal condition.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"7 1","pages":"57-64"},"PeriodicalIF":0.2,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44302352","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}
Pub Date : 2017-12-01DOI: 10.22108/IJGT.2017.21223
A. Staroletov
The set of element orders of a finite group $G$ is called the {em spectrum}. Groups with coinciding spectra are said to be {em isospectral}. It is known that if $G$ has a nontrivial normal soluble subgroup then there exist infinitely many pairwise non-isomorphic groups isospectral to $G$. The situation is quite different if $G$ is a nonabelain simple group. Recently it was proved that if $L$ is a simple classical group of dimension at least 62 and $G$ is a finite group isospectral to $L$, then up to isomorphism $Lleq GleqAut L$. We show that the assertion remains true if 62 is replaced by 38.
{"title":"On almost recognizability by spectrum of simple classical groups","authors":"A. Staroletov","doi":"10.22108/IJGT.2017.21223","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21223","url":null,"abstract":"The set of element orders of a finite group $G$ is called the {em spectrum}. Groups with coinciding spectra are said to be {em isospectral}. It is known that if $G$ has a nontrivial normal soluble subgroup then there exist infinitely many pairwise non-isomorphic groups isospectral to $G$. The situation is quite different if $G$ is a nonabelain simple group. Recently it was proved that if $L$ is a simple classical group of dimension at least 62 and $G$ is a finite group isospectral to $L$, then up to isomorphism $Lleq GleqAut L$. We show that the assertion remains true if 62 is replaced by 38.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"6 1","pages":"7-33"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46060019","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}
Pub Date : 2017-12-01DOI: 10.22108/IJGT.2017.21222
Hamid Mousavi, Zahra Rezazadeh
For a finite group $G$, let $nu_{nc}(G)$ denote the number of conjugacy classes of non-normal non-cyclic subgroups of $G$. We characterize the finite non-nilpotent groups whose all non-normal non-cyclic subgroups are conjugate.
{"title":"Finite non-nilpotent groups with few non-normal non-cyclic subgroups","authors":"Hamid Mousavi, Zahra Rezazadeh","doi":"10.22108/IJGT.2017.21222","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21222","url":null,"abstract":"For a finite group $G$, let $nu_{nc}(G)$ denote the number of conjugacy classes of non-normal non-cyclic subgroups of $G$. We characterize the finite non-nilpotent groups whose all non-normal non-cyclic subgroups are conjugate.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"6 1","pages":"35-40"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46530439","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}
Pub Date : 2017-12-01DOI: 10.22108/IJGT.2017.21233
B. Ebrahimzadeh, A. Iranmanesh, H. P. Mosaed
In this paper, we prove that Ree group ${}^2G_2(q)$, where $qpmsqrt{3q}+1$ is a prime number can be uniquely determined by the order of group and the number of elements with the same order.
{"title":"A new characterization of Ree group $mathbf{{}^2G_2(q)}$ by the order of group and the number of elements with the same order","authors":"B. Ebrahimzadeh, A. Iranmanesh, H. P. Mosaed","doi":"10.22108/IJGT.2017.21233","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21233","url":null,"abstract":"In this paper, we prove that Ree group ${}^2G_2(q)$, where $qpmsqrt{3q}+1$ is a prime number can be uniquely determined by the order of group and the number of elements with the same order.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"6 1","pages":"1-6"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46878751","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}
Pub Date : 2017-12-01DOI: 10.22108/IJGT.2017.21477
Z. Mpono
$M_{24}$ is the largest Mathieu sporadic simple group of order $244 823 040 = 2^{10} {cdot} 3^3 {cdot} 5 {cdot} 7 {cdot} 11 {cdot} 23$ and contains all the other Mathieu sporadic simple groups as subgroups. The object in this paper is to study the ranks of $M_{24}$ with respect to the conjugacy classes of all its nonidentity elements.
{"title":"The conjugacy class ranks of $M_{24}$","authors":"Z. Mpono","doi":"10.22108/IJGT.2017.21477","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21477","url":null,"abstract":"$M_{24}$ is the largest Mathieu sporadic simple group of order $244 823 040 = 2^{10} {cdot} 3^3 {cdot} 5 {cdot} 7 {cdot} 11 {cdot} 23$ and contains all the other Mathieu sporadic simple groups as subgroups. The object in this paper is to study the ranks of $M_{24}$ with respect to the conjugacy classes of all its nonidentity elements.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"6 1","pages":"53-58"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48102858","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：