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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.08617 |
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| _version_ | 1866915124587003904 |
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| author | Du, Shaofei Yu, Hao Luo, Wenjuan |
| author_facet | Du, Shaofei Yu, Hao Luo, Wenjuan |
| contents | Let $X(Q)=QC$ be a group, where $Q$ is a generalized quaternion group and $C$ is a cyclic group such that $Q\cap C=1$. In this paper, $X(Q)$ will be characterized and moreover, a complete classification for that will be given, provided $C$ is core-free. For the reason of self-constraint, in this paper a classification of the group $X(D)=DC$ is also given, where $D$ is a dihedral group and $C$ is a cyclic group such that $D\cap C=1$ and $C$ is core-free. Remind that the group $X(D)$ was recently classified in [12], based on a number of papers on skew-morphisms of dihedral groups. In this paper, a different approach from that in [12] will be used. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08617 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Product of a Generalized Quaternion Group And a Cyclic Group Du, Shaofei Yu, Hao Luo, Wenjuan Group Theory Let $X(Q)=QC$ be a group, where $Q$ is a generalized quaternion group and $C$ is a cyclic group such that $Q\cap C=1$. In this paper, $X(Q)$ will be characterized and moreover, a complete classification for that will be given, provided $C$ is core-free. For the reason of self-constraint, in this paper a classification of the group $X(D)=DC$ is also given, where $D$ is a dihedral group and $C$ is a cyclic group such that $D\cap C=1$ and $C$ is core-free. Remind that the group $X(D)$ was recently classified in [12], based on a number of papers on skew-morphisms of dihedral groups. In this paper, a different approach from that in [12] will be used. |
| title | The Product of a Generalized Quaternion Group And a Cyclic Group |
| topic | Group Theory |
| url | https://arxiv.org/abs/2305.08617 |