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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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| _version_ | 1866911783104544768 |
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| author | Chen, Haimiao Xiong, Yueshan Zhu, Zhongjian |
| author_facet | Chen, Haimiao Xiong, Yueshan Zhu, Zhongjian |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1506_02234 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Automorphisms of metacyclic groups Chen, Haimiao Xiong, Yueshan Zhu, Zhongjian Group Theory 20D45 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. |
| title | Automorphisms of metacyclic groups |
| topic | Group Theory 20D45 |
| url | https://arxiv.org/abs/1506.02234 |