发表机构
Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University; Department of Mathematics, School of Science and Engineering, Waseda University（大阪中央高等数学研究所，大阪公立大学; 早稻田大学理工学术院数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入满射拟群同态的相对内自同构群和相对换位群，定义连通同态并建立最大连通覆盖分解，最后分类有限纤维的拟群结构。
AI 中文摘要
本文介绍了与满射拟群同态相关的内自同构群和换位群的相对版本。利用相对内自同构群，我们定义了满射同态的\emph{连通性}概念。我们将连通同态代数地刻画为商映射，并利用相对换位群为任意满射建立了一个最大的\emph{连通覆盖}分解。最后，我们研究了相对内自同构群在每个纤维上作用为$2$-传递的满射同态。在此假设下，我们分类了有限纤维可能的拟群结构。
英文摘要
This paper introduces relative versions of the inner automorphism group and the transvection group associated with surjective quandle homomorphisms. By using the relative inner automorphism group, we define a notion of connectedness for surjective homomorphisms. We characterize connected homomorphisms algebraically as quotient maps, and use the relative transvection group to establish a maximal connected--covering factorization for arbitrary surjections. We also introduce strongly connected homomorphisms via the relative transvection group, and classify them in terms of perfect normal subgroups of inner automorphism groups. A later part of this paper studies surjective homomorphisms for which the relative inner automorphism group acts $2$-transitively on each fiber. Under this assumption, we classify the possible quandle structures of the finite fibers.
Comments49 pages. v2: Corrected an error in Proposition 2.14 of v1; major updates throughout
