Zappa-Szép 群积的自同构的行列式
Determinant for automorphisms of Zappa-Szép product of groups
AI总结：
本文利用映射的2×2矩阵描述，研究两个群Zappa-Szép积的自同态行列式，刻画可逆自同态，并计算交错群A5的行列式。
AI中文摘要：
在文献[detsem]中，讨论了将两个群的Zappa-Szép积的自同态描述为映射的$2\ imes 2$矩阵群。利用这一描述，我们研究了两个群的Zappa-Szép积的自同态的行列式概念。借助行列式开发的工具，给出了可逆自同态的一个刻画。还计算了交错群$A_{5}$的行列式。
英文摘要：
A description of the endomorphisms of Zappa-Szép products of two groups as a group of $2\times 2$ matrices of maps is discussed in \cite{detsem}. Using this description, we have studied the concept of determinant for the endomorphisms of Zappa-Szép products of two groups. A characterization of the invertible endomorphisms is given with the help of the tools developed using the determinants. The determinants are also computed for the alternating group $A_{5}$.
