发布求助
文献互助 智能选刊 最新文献

Groups Complex. Cryptol.最新文献

筛选
英文 中文
Authentication from Matrix Conjugation 矩阵共轭的认证
Groups Complex. Cryptol. Pub Date : 2010-10-24 DOI: 10.1515/GCC.2009.199
D. Grigoriev, V. Shpilrain
{"title":"Authentication from Matrix Conjugation","authors":"D. Grigoriev, V. Shpilrain","doi":"10.1515/GCC.2009.199","DOIUrl":"https://doi.org/10.1515/GCC.2009.199","url":null,"abstract":"We propose an authentication scheme where forgery (a.k.a. impersonation) seems infeasible without finding the prover's long-term private key. The latter would follow from solving the conjugacy search problem in the platform (noncommutative) semigroup, i.e., to recovering X from X –1 AX and A. The platform semigroup that we suggest here is the semigroup of n × n matrices over truncated multivariable polynomials over a ring.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134304656","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: 32
Search and witness problems in group theory 群论中的搜索和见证问题
Groups Complex. Cryptol. Pub Date : 2010-10-03 DOI: 10.1515/gcc.2010.015
V. Shpilrain
{"title":"Search and witness problems in group theory","authors":"V. Shpilrain","doi":"10.1515/gcc.2010.015","DOIUrl":"https://doi.org/10.1515/gcc.2010.015","url":null,"abstract":"Abstract Decision problems are problems of the following nature: given a property and an object , find out whether or not the object has the property . On the other hand, witness problems are: given a property and an object with the property , find a proof of the fact that indeed has the property . On the third hand(?!), search problems are of the following nature: given a property and an object with the property , find something “material” establishing the property ; for example, given two conjugate elements of a group, find a conjugator. In this survey our focus is on various search problems in group theory, including the word search problem, the subgroup membership search problem, the conjugacy search problem, and others.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130510534","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
How to compute the Wedderburn decomposition of a finite-dimensional associative algebra 如何计算有限维关联代数的Wedderburn分解
Groups Complex. Cryptol. Pub Date : 2010-08-11 DOI: 10.1515/gcc.2011.003
M. Bremner
{"title":"How to compute the Wedderburn decomposition of a finite-dimensional associative algebra","authors":"M. Bremner","doi":"10.1515/gcc.2011.003","DOIUrl":"https://doi.org/10.1515/gcc.2011.003","url":null,"abstract":"Abstract This is a survey paper on algorithms that have been developed during the last 25 years for the explicit computation of the structure of an associative algebra of finite dimension over either a finite field or an algebraic number field. This constructive approach was initiated in 1985 by Friedl and Rónyai and has since been developed by Cohen, de Graaf, Eberly, Giesbrecht, Ivanyos, Küronya and Wales. I illustrate these algorithms with the case n = 2 of the rational semigroup algebra of the partial transformation semigroup PTn on n elements; this generalizes the full transformation semigroup and the symmetric inverse semigroup, and these generalize the symmetric group Sn .","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131779431","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: 23
The diameter of a random Cayley graph of ℤ q 随机Cayley图的直径
Groups Complex. Cryptol. Pub Date : 2010-06-01 DOI: 10.1515/gcc.2010.004
Gideon Amir, O. Gurel-Gurevich
{"title":"The diameter of a random Cayley graph of ℤ q","authors":"Gideon Amir, O. Gurel-Gurevich","doi":"10.1515/gcc.2010.004","DOIUrl":"https://doi.org/10.1515/gcc.2010.004","url":null,"abstract":"Abstract Consider the Cayley graph of the cyclic group of prime order q with k uniformly chosen generators. For fixed k, we prove that the diameter of said graph is asymptotically (in q) of order . This answers a question of Benjamini. The same also holds when the generating set is taken to be a symmetric set of size 2k.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"14 1-2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133036869","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: 12
Cutting up graphs revisited – a short proof of Stallings' structure theorem 重新审视分割图——斯托林斯结构定理的简短证明
Groups Complex. Cryptol. Pub Date : 2010-03-04 DOI: 10.1515/gcc.2010.013
B. Krön
{"title":"Cutting up graphs revisited – a short proof of Stallings' structure theorem","authors":"B. Krön","doi":"10.1515/gcc.2010.013","DOIUrl":"https://doi.org/10.1515/gcc.2010.013","url":null,"abstract":"Abstract This is a short proof of the existence of finite sets of edges in graphs with more than one end, such that after removing them we obtain two components which are nested with all their isomorphic images. This was first done in “Cutting up graphs” [Dunwoody, Combinatorica 2: 15–23, 1982]. Together with a certain tree construction and some elementary Bass–Serre theory this yields a combinatorial proof of Stallings' theorem on the structure of finitely generated groups with more than one end.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128017507","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: 19
Subgroups of R. Thompson's group F that are isomorphic to F r·汤普森的子组群同构的F
Groups Complex. Cryptol. Pub Date : 2009-12-03 DOI: 10.1515/gcc.2011.009
B. Wassink
{"title":"Subgroups of R. Thompson's group F that are isomorphic to F","authors":"B. Wassink","doi":"10.1515/gcc.2011.009","DOIUrl":"https://doi.org/10.1515/gcc.2011.009","url":null,"abstract":"Abstract Richard Thompson's group F has a two generator presentation This paper studies when a pair of elements in F consists of the images of the generators x 0 and x 1 under a self monomorphism.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128825780","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 Cayley graphs of virtually free groups 在几乎自由群体的Cayley图上
Groups Complex. Cryptol. Pub Date : 2009-11-11 DOI: 10.1515/gcc.2011.012
Yago Antolín
{"title":"On Cayley graphs of virtually free groups","authors":"Yago Antolín","doi":"10.1515/gcc.2011.012","DOIUrl":"https://doi.org/10.1515/gcc.2011.012","url":null,"abstract":"Abstract In 1985, Dunwoody showed that finitely presentable groups are accessible. Dunwoody's result was used to show that context-free groups, groups quasi-isometric to trees or finitely presentable groups of asymptotic dimension 1 are virtually free. Using another theorem of Dunwoody of 1979, we study when a group is virtually free in terms of its Cayley graph, and we obtain new proofs of the mentioned results and others previously depending on these.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115456583","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: 21
Torsion-free Abelian Factor Groups of the Baumslag-Solitar Groups and Subgroups of the Additive Group of the Rational Numbers 有理数加性群的baumslag -孤群和子群的无扭Abelian因子群
Groups Complex. Cryptol. Pub Date : 2009-10-01 DOI: 10.1515/GCC.2009.165
A. Clement
{"title":"Torsion-free Abelian Factor Groups of the Baumslag-Solitar Groups and Subgroups of the Additive Group of the Rational Numbers","authors":"A. Clement","doi":"10.1515/GCC.2009.165","DOIUrl":"https://doi.org/10.1515/GCC.2009.165","url":null,"abstract":"The object of this paper is to give a proof of the following theorem: S/P ≅ Λ mn ⊆ ℚ+, where S/P is a certain torsion-free factor group of the Baumslag-Solitar group 〈a, b; a –1 bma = bn | m ≠ 0, n ≠ 0, m, n ∈ ℤ〉, with m and n are relatively prime, and Λ mn is a subgroup of the additive group of the rational numbers ℚ+.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133731430","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
Presentations of matrix rings 矩阵环的表示
Groups Complex. Cryptol. Pub Date : 2009-07-21 DOI: 10.1515/gcc.2010.003
M. Kassabov
{"title":"Presentations of matrix rings","authors":"M. Kassabov","doi":"10.1515/gcc.2010.003","DOIUrl":"https://doi.org/10.1515/gcc.2010.003","url":null,"abstract":"Abstract We construct a short presentation of the ring of n × n matrices over Z with only 2 generators and 3 relations.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123141894","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: 4
Some geodesic problems in groups 群中的一些测地线问题
Groups Complex. Cryptol. Pub Date : 2009-07-20 DOI: 10.1515/gcc.2010.014
M. Elder, A. Rechnitzer
{"title":"Some geodesic problems in groups","authors":"M. Elder, A. Rechnitzer","doi":"10.1515/gcc.2010.014","DOIUrl":"https://doi.org/10.1515/gcc.2010.014","url":null,"abstract":"Abstract We consider several algorithmic problems concerning geodesics in finitely generated groups. We show that the three geodesic problems considered by Miasnikov et al. are polynomial-time reducible to each other. We study two new geodesic problems which arise in a previous paper of the authors and Fusy.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"863 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117143071","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: 12
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