浙江大学学报（理学版）2026，Vol.53Issue(4)：415-422,8.DOI:10.3785/1008-9497.25069
亚同态与群论定理的证明
Subhomomorphisms and proofs of group theoretical theorems
摘要
Abstract
The concept of subhomomorphism is proposed through the introduction of conjugate mapping.Definitions are provided for the sets of subhomomorphisms and X-homomorphisms.Analysis on the action of groups on the set of subhomomorphisms is conducted,leading to the establishment of the orbit equation.Fundamental algebraic methods are employed to derive the congruence relations satisfied by the number of homomorphisms.This derivation enables the determination of non-trivial homomorphisms within the set of subhomomorphisms.As an application of the developed theoretical framework,a proof of the Schur-Zassenhaus theorem is presented.关键词
亚同态/群作用/Schur-Zassenhaus定理Key words
subhomomorphism/group action/Schur-Zassenhaus theorem分类
数理科学引用本文复制引用
王兆权..亚同态与群论定理的证明[J].浙江大学学报（理学版）,2026,53(4):415-422,8.基金项目
青岛滨海学院教学改革研究项目(2024JY12). （2024JY12）
