Automorphisms of metacyclic groups

Haimiao Chen, Yueshan Xiong, Zhongjian Zhu

A metacyclic group $H$ can be presented as $⟨\alpha ,\beta \mid {\alpha }^n=1,{\beta }^m={\alpha }^t,\beta \alpha {\beta }^{-1}={\alpha }^r⟩$ for some $n,m,t,r$. Each endomorphism $\sigma$ of $H$ is determined by $σ(α)…