有限群满同态测试的算法
Algorithms for Finite Group Epimorphism Testing
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中文总结 AI 辅助
本文针对几类结构化有限群，提出了多项式时间的群满同态测试算法，解决了这些类上满同态问题的复杂性。这些类此前已知具有多项式时间同构测试，包括具有循环补的交换正规Hall子群等。该工作推进了有限群满同态问题的算法研究。
中文摘要 AI 辅助
群满同态问题（GpEpi）询问，给定两个有限群$G_1$和$G_2$，是否存在从$G_1$到$G_2$的满射群同态，即满同态。当输入群由其乘法（Cayley）表给出时，该问题在一般情况下具有拟多项式时间算法，但对其在结构化有限群类上的复杂性知之甚少。本文研究了GpEpi在几个被广泛研究的有限群类上的计算复杂性。我们的主要结果是针对几个先前已知具有多项式时间同构测试的群类给出了多项式时间满同态测试：具有循环补的交换正规Hall子群的群；具有（乘积）初等交换正规Hall子群且补为初等交换的群；以及对其交换主因子有一定限制的群。
英文摘要
The Group Epimorphism Problem (GpEpi) asks, given two finite groups $G_1$ and $G_2$, whether there exists a surjective group homomorphism, or epimorphism, from $G_1$ to $G_2$. When the input groups are given by their multiplication (Cayley) tables, the problem admits a quasipolynomial-time algorithm in general, but little is known about its complexity for structured classes of finite groups. In this paper, we study the computational complexity of GpEpi for several well-studied classes of finite groups. Our main results are polynomial-time epimorphism tests for several classes of groups for which polynomial-time isomorphism testing was previously known: Groups with Abelian normal Hall subgroups with cyclic complement; Groups with (product of) elementary Abelian normal Hall subgroup with elementary Abelian complement; and Groups with some constraints on their Abelian chief factors.
发表机构
- University of Colorado Boulder（科罗拉多大学博尔德分校）
- Indian Institute of Information Technology Vadodara（瓦多达拉信息研究所）
- Nagoya University（名古屋大学）
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