亚同态与群论定理的证明OA

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.