检索结果-南通市图书馆

On Isomorphism Testing of Groups with normal hall subgroups

Journal of Computer Science & Technology 2012年第4期27卷 687-701页

作者：乔友明 Jayalal Sarma M.N 唐邦晟 Institute for Theoretical Computer Science Tsinghua University Department of Computer Science and Engineering Indian Institute of Technology Madras

A normal hall subgroup N of a group G is a normal subgroup with its order coprime with its index. Schur- Zassenhaus theorem states that every normal hall subgroup has a complement subgroup, that is a set of coset representatives H which also forms a subgroup of G. In this paper, we present a framework to test isomorphism of groups with at least one normal hall subgroup, when groups are given as multiplication tables. To establish the framework, we first observe that a proof of Schur-Zassenhaus theorem is constructive, and formulate a necessary and sufficient condition for testing isomorphism in terms of the associated actions of the semidirect products, and isomorphisms of the normal parts and complement parts. We then focus on the case when the normal subgroup is abelian. Utilizing basic facts of representation theory of finite groups and a technique by Le Gall （STACS 2009）, we first get an efficient isomorphism testing algorithm when the complement has bounded number of generators. For the case when the complement subgroup is elementary abelian, which does not necessarily have bounded number of generators, we obtain a polynomial time isomorphism testing algorithm by reducing to generalized code isomorphism problem, which asks whether two linear subspaces are the same up to permutation of coordinates. A solution to the latter can be obtained by a mild extension of the singly exponential （in the number of coordinates） time algorithm for code isomorphism problem developed recently by Babai et al. （SODA 2011）. Enroute to obtaining the above reduction, we study the following computational problem in representation theory of finite groups： given two representations ρandτ- of a group H over Zp^d, a prime, determine if there exists an automorphism ： ФH→ H, such that the induced representation p Ф= ρ o Ф and τ are equivalent, in time poly（｜H｜, p^d）.

关键词： group isomorphism normal hall subgroup isomorphism testing problem complexity

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

欢迎您,

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：