关于半直积同构的讨论

Discussion on the Isomorphism of the Semidirect Product

这篇文章从半直积的定义出发,给出了当群H或当从群H到N的自同构群Aut(N)的两个同态φ,ψ满足一定条件时半直积N∝φH与N∝ψH同构的两个定理,而其中一个定理是一个已知结果的推广.

We give two theorems about the isomorphism between the semidirect product of N by H corresponding to φand that of N by H corresponding to ψ, which the group H or two homorphism φ,ψ from the group H to the Aut（N） satisfies some condition. One of the theorem extend a well-known result.