Abstract
A metacyclic group H can be presented as 〈α,β: αn = 1, βm = αt, βαβ−1 = αr〉 for some n, m, t, r. Each endomorphism σ of H is determined by \(\sigma(\alpha)=\alpha^{x_1}\beta^{y_1}, \sigma(\beta)=\alpha^{x_2}\beta^{y_2}\) for some integers x1, x2, y1, y2. We give sufficient and necessary conditions on x1, x2, y1, y2 for σ to be an automorphism.
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Chen, H., Xiong, Y. & Zhu, Z. Automorphisms of metacyclic groups. Czech Math J 68, 803–815 (2018). https://doi.org/10.21136/CMJ.2017.0656-16
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DOI: https://doi.org/10.21136/CMJ.2017.0656-16