Groups Complex. Cryptol.最新文献_第5页

A Diffie–Hellman key exchange protocol using matrices over noncommutative rings 非交换环上使用矩阵的Diffie-Hellman密钥交换协议

Groups Complex. Cryptol. Pub Date : 1900-01-01 DOI: 10.1515/gcc-2012-0001

Mohammad Eftekhari

引用次数: 22

Algebraic attacks using SAT-solvers 使用sat求解器的代数攻击

Groups Complex. Cryptol. Pub Date : 1900-01-01 DOI: 10.1515/gcc.2010.016

Philipp Jovanovic, M. Kreuzer

引用次数: 35

Existence and Non-Existence of Torsion in Maximal Arithmetic Fuchsian Groups 极大算术Fuchsian群中扭的存在性与不存在性

Groups Complex. Cryptol. Pub Date : 1900-01-01 DOI: 10.1515/GCC.2009.287

C. Maclachlan

{"title":"Existence and Non-Existence of Torsion in Maximal Arithmetic Fuchsian Groups","authors":"C. Maclachlan","doi":"10.1515/GCC.2009.287","DOIUrl":"https://doi.org/10.1515/GCC.2009.287","url":null,"abstract":"In [1], Borel discussed discrete arithmetic groups arising from quaternion algebras over number fields with particular reference to arithmetic Kleinian and arithmetic Fuchsian groups. In these cases, he described, in each commensurability class, a class of groups which contains all maximal groups. Developing results on embedding commutative orders of the defining number field into maximal or Eichler orders in the defining quaternion algebra, Chinburg and Friedman [2] stated necessary and sufficient conditions for the existence of torsion in this class of groups in terms of the defining arithmetic data. This was more fully explored in the case of Kleinian groups in [3]. In the case of Fuchsian groups, these results on the existence of torsion were extended to obtain formulas for the number of conjugacy classes of finite cyclic subgroups for each group in this class [8, 9]. In this paper, we examine, across the range of arithmetic Fuchsian groups, how widespread torsion is in maximal Fuchsian groups. Some studies in low genus cases (see e.g. [7, 12]) indicate that 2-torsion is very prevalent. The results obtained here substantiate that but we will also obtain maximal arithmetic Fuchsian groups which are torsion-free. The author is grateful to Alan Reid for conversations on parts of this paper.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123619330","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: 9

An update on Hurwitz groups Hurwitz小组的最新进展

Groups Complex. Cryptol. Pub Date : 1900-01-01 DOI: 10.1515/gcc.2010.002

M. Conder

引用次数: 50

A Note on the Shifted Conjugacy Problem in Braid Groups 关于辫状群中移位共轭问题的一个注记

Groups Complex. Cryptol. Pub Date : 1900-01-01 DOI: 10.1515/GCC.2009.227

A. Kalka, E. Liberman, M. Teicher

引用次数: 11

Power-Commutative Nilpotent R-Powered Groups 幂交换幂幂r幂群

Groups Complex. Cryptol. Pub Date : 1900-01-01 DOI: 10.1515/GCC.2009.297

S. Majewicz, Marcos Zyman