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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2015
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1506.02234 |
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Table of Contents:
- A metacyclic group $H$ can be presented as $\langle α,β\mid α^{n}=1, \ β^{m}=α^{t}, \ βαβ^{-1}=α^{r}\rangle$ for some $n,m,t,r$. Each endomorphism $σ$ of $H$ is determined by $σ(α)=α^{x_{1}}β^{y_{1}}, σ(β)=α^{x_{2}}β^{y_{2}}$ for some integers $x_{1},x_{2},y_{1},y_{2}$. We give sufficient and necessary conditions on $x_{1},x_{2},y_{1},y_{2}$ for $σ$ to be an automorphism.