Pub Date : 2019-07-10DOI: 10.22108/IJGT.2018.112439.1494
B. Fine, A. Moldenhauer, Gerhard Rosneberger
Groups of F -type were introduced in [B. Fine and G. Rosenberger, Generalizing Algebraic Properties of Fuchsian Groups, London Math. Soc. Lecture Note Ser., 159 (1991) 124–147.] as a natural algebraic generalization of Fuchsian groups. They can be considered as the analogs of cyclically pinched one-relator groups where torsion is allowed. Using the methods In [B. Fine. M. Kreuzer and G. Rosenberger, Faithful Real Representations of Cyclically Pinched One-Relator Groups, Int. J. Group Theory, 3 (2014) 1–8.] we prove that any hyperbolic group of F -type has a faithful representation in PSL(2,R). From this we also obtain that a cyclically pinched one-relator group has a faithful real representation if and only if it is hyperbolic. We further survey the many nice properties of groups of F -type.
{"title":"Faithful Real Representations of Groups of $F$-type","authors":"B. Fine, A. Moldenhauer, Gerhard Rosneberger","doi":"10.22108/IJGT.2018.112439.1494","DOIUrl":"https://doi.org/10.22108/IJGT.2018.112439.1494","url":null,"abstract":"Groups of F -type were introduced in [B. Fine and G. Rosenberger, Generalizing Algebraic Properties of Fuchsian Groups, London Math. Soc. Lecture Note Ser., 159 (1991) 124–147.] as a natural algebraic generalization of Fuchsian groups. They can be considered as the analogs of cyclically pinched one-relator groups where torsion is allowed. Using the methods In [B. Fine. M. Kreuzer and G. Rosenberger, Faithful Real Representations of Cyclically Pinched One-Relator Groups, Int. J. Group Theory, 3 (2014) 1–8.] we prove that any hyperbolic group of F -type has a faithful representation in PSL(2,R). From this we also obtain that a cyclically pinched one-relator group has a faithful real representation if and only if it is hyperbolic. We further survey the many nice properties of groups of F -type.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44441794","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 : 2019-06-18DOI: 10.22108/IJGT.2019.113029.1502
Hoshang Behravesh, M. Ghaffarzadeh, M. Ghasemi, Somayeh Hekmatara
In this paper we prove that some Janko groups are uniquely determined by their orders and one irreducible character degree. Also we prove that some finite simple K4-groups are uniquely determined by their character degree graphs and their orders.
{"title":"Recognition of Janko groups and some simple $K_4$-groups by the order and one irreducible character degree or character degree graph","authors":"Hoshang Behravesh, M. Ghaffarzadeh, M. Ghasemi, Somayeh Hekmatara","doi":"10.22108/IJGT.2019.113029.1502","DOIUrl":"https://doi.org/10.22108/IJGT.2019.113029.1502","url":null,"abstract":"In this paper we prove that some Janko groups are uniquely determined by their orders and one irreducible character degree. Also we prove that some finite simple K4-groups are uniquely determined by their character degree graphs and their orders.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48898314","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 : 2019-06-01DOI: 10.22108/IJGT.2017.108014.1455
Juliane Hansmann
Let $K$ be a commutative ring with identity and $N$ the free nilpotent $K$-algebra on a non-empty set $X$. Then $N$ is a group with respect to the circle composition. We prove that the subgroup generated by $X$ is relatively free in a suitable class of groups, depending on the choice of $K$. Moreover, we get unique representations of the elements in terms of basic commutators. In particular, if $K$ is of characteristic $0$ the subgroup generated by $X$ is freely generated by $X$ as a nilpotent group.
{"title":"On free subgroups of finite exponent in circle groups of free nilpotent algebras","authors":"Juliane Hansmann","doi":"10.22108/IJGT.2017.108014.1455","DOIUrl":"https://doi.org/10.22108/IJGT.2017.108014.1455","url":null,"abstract":"Let $K$ be a commutative ring with identity and $N$ the free nilpotent $K$-algebra on a non-empty set $X$. Then $N$ is a group with respect to the circle composition. We prove that the subgroup generated by $X$ is relatively free in a suitable class of groups, depending on the choice of $K$. Moreover, we get unique representations of the elements in terms of basic commutators. In particular, if $K$ is of characteristic $0$ the subgroup generated by $X$ is freely generated by $X$ as a nilpotent group.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"8 1","pages":"29-40"},"PeriodicalIF":0.2,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43468139","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 : 2019-06-01DOI: 10.22108/IJGT.2017.103226.1424
Z. Akhlaghi, M. Khatami, B. Khosravi
Let (G) be a finite group. The character degree graph of (G), which is denoted by (Gamma (G)), is the graph whose vertices are the prime divisors of the character degrees of the group (G) and two vertices (p_1) and (p_2) are joined by an edge if (p_1p_2) divides some character degree of (G). In this paper we prove that the simple group (mathrm{PSL}(2,p^2) ) is uniquely determined by its character degree graph and its order. Let (X_1(G)) be the set of all irreducible complex character degrees of (G) counting multiplicities. As a consequence of our results we prove that if (G) is a finite group such that (X_1(G)=X_1(mathrm{PSL}(2,p^2) )), then (Gcong mathrm{PSL}(2,p^2) ). This implies that (mathrm{PSL}(2,p^2) ) is uniquely determined by the structure of its complex group algebra.
{"title":"Recognition of the simple groups $PSL_2(q)$ by character degree graph and order","authors":"Z. Akhlaghi, M. Khatami, B. Khosravi","doi":"10.22108/IJGT.2017.103226.1424","DOIUrl":"https://doi.org/10.22108/IJGT.2017.103226.1424","url":null,"abstract":"Let (G) be a finite group. The character degree graph of (G), which is denoted by (Gamma (G)), is the graph whose vertices are the prime divisors of the character degrees of the group (G) and two vertices (p_1) and (p_2) are joined by an edge if (p_1p_2) divides some character degree of (G). In this paper we prove that the simple group (mathrm{PSL}(2,p^2) ) is uniquely determined by its character degree graph and its order. Let (X_1(G)) be the set of all irreducible complex character degrees of (G) counting multiplicities. As a consequence of our results we prove that if (G) is a finite group such that (X_1(G)=X_1(mathrm{PSL}(2,p^2) )), then (Gcong mathrm{PSL}(2,p^2) ). This implies that (mathrm{PSL}(2,p^2) ) is uniquely determined by the structure of its complex group algebra.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"8 1","pages":"41-46"},"PeriodicalIF":0.2,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48762173","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 : 2019-05-02DOI: 10.22108/IJGT.2019.115382.1532
Leire Legarreta, N. Gavioli, C. M. Scoppola, Marco Ruscitti
In this paper we analyse properties satisfied by certain open normal subgroups in normally constrained pro-$p$ groups and in a spread version of normally constrained pro-$p$ groups. In the case of powerful normally constrained pro-$p$ groups, we exhibit some kind of inheritance properties in certain open normal subgroups.
{"title":"Open normal subgroups in normally constrained pro-p groups","authors":"Leire Legarreta, N. Gavioli, C. M. Scoppola, Marco Ruscitti","doi":"10.22108/IJGT.2019.115382.1532","DOIUrl":"https://doi.org/10.22108/IJGT.2019.115382.1532","url":null,"abstract":"In this paper we analyse properties satisfied by certain open normal subgroups in normally constrained pro-$p$ groups and in a spread version of normally constrained pro-$p$ groups. In the case of powerful normally constrained pro-$p$ groups, we exhibit some kind of inheritance properties in certain open normal subgroups.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"9 1","pages":"125-132"},"PeriodicalIF":0.2,"publicationDate":"2019-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42228951","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 : 2019-04-13DOI: 10.22108/IJGT.2019.115685.1535
S. Y. Madanha
{"title":"Weakly totally permutable products and Fitting classes","authors":"S. Y. Madanha","doi":"10.22108/IJGT.2019.115685.1535","DOIUrl":"https://doi.org/10.22108/IJGT.2019.115685.1535","url":null,"abstract":"","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2019-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45817174","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 : 2019-03-07DOI: 10.22108/IJGT.2019.113180.1506
D. D’Angeli, E. Rodaro, A. Donno
Fragile words have been already considered in the context of automata groups. Here we focus our attention on a special class of strongly fragile words that we call Catalan fragile words. Among other properties, we show that there exists a one-to-one correspondence between the set of Catalan fragile words and the set of full binary trees.
{"title":"Catalan fragile words","authors":"D. D’Angeli, E. Rodaro, A. Donno","doi":"10.22108/IJGT.2019.113180.1506","DOIUrl":"https://doi.org/10.22108/IJGT.2019.113180.1506","url":null,"abstract":"Fragile words have been already considered in the context of automata groups. Here we focus our attention on a special class of strongly fragile words that we call Catalan fragile words. Among other properties, we show that there exists a one-to-one correspondence between the set of Catalan fragile words and the set of full binary trees.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"9 1","pages":"69-80"},"PeriodicalIF":0.2,"publicationDate":"2019-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46484509","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 : 2019-03-07DOI: 10.22108/IJGT.2019.115244.1529
Leire Legarreta, M. Tota
We consider conditions on normalizers or centralizers in a group and we collect results showing how such conditions influence the structure of the group.
我们考虑组中归一化器或中心化器的条件，并收集显示这些条件如何影响组结构的结果。
{"title":"A survey on groups with some restrictions on normalizers or centralizers","authors":"Leire Legarreta, M. Tota","doi":"10.22108/IJGT.2019.115244.1529","DOIUrl":"https://doi.org/10.22108/IJGT.2019.115244.1529","url":null,"abstract":"We consider conditions on normalizers or centralizers in a group and we collect results showing how such conditions influence the structure of the group.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"9 1","pages":"113-124"},"PeriodicalIF":0.2,"publicationDate":"2019-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47735519","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 : 2019-03-07DOI: 10.22108/IJGT.2019.111448.1480
A. Beltrán, M. J. Felipe, C. Melchor
We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that have only been partially solved.
{"title":"SOME PROBLEMS ABOUT PRODUCTS OF CONJUGACY CLASSES IN FINITE GROUPS","authors":"A. Beltrán, M. J. Felipe, C. Melchor","doi":"10.22108/IJGT.2019.111448.1480","DOIUrl":"https://doi.org/10.22108/IJGT.2019.111448.1480","url":null,"abstract":"We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that have only been partially solved.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"9 1","pages":"59-68"},"PeriodicalIF":0.2,"publicationDate":"2019-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45042054","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 : 2019-03-01DOI: 10.22108/IJGT.2018.109973.1471
M. Ibrahim, Faryad Ali, M. Al-Kadhi, A. Aljouiee
{"title":"On the ranks of Fischer group $Fi_{24}^{,prime}$ and the Baby Monster group $mathbb{B}$","authors":"M. Ibrahim, Faryad Ali, M. Al-Kadhi, A. Aljouiee","doi":"10.22108/IJGT.2018.109973.1471","DOIUrl":"https://doi.org/10.22108/IJGT.2018.109973.1471","url":null,"abstract":"","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"8 1","pages":"11-22"},"PeriodicalIF":0.2,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44338097","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：