Problem
Research questions and friction points this paper is trying to address.
Finite Group
Epimorphism
Computational Complexity
Algorithms for Finite Group Epimorphism Testing
🤖 AI Summary
本文研究了有限群同态测试问题，针对具有特定结构的有限群类，提出了多项式时间算法以判断是否存在满同态。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
polynomial-time epimorphism tests
finite groups
Abelian normal Hall subgroups
elementary Abelian complements
computational complexity
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