Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912356847583232 |
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| author | Lu, Jiaping Quick, Martyn |
| author_facet | Lu, Jiaping Quick, Martyn |
| contents | Let $G_{1}$, $G_{2}$, ... be a sequence of groups each of which is either an alternating group, a symmetric group or a cyclic group and construct a sequence $(W_{i})$ of wreath products via $W_{1} = G_{1}$ and, for each $i \geq 1$, $W_{i+1} = G_{i+1} \operatorname{wr} G_{i}$ via the natural permutation action. We determine the minimum number $d(W_{i})$ of generators required for each wreath product in this sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups Lu, Jiaping Quick, Martyn Group Theory 20E22 20F05 20D06 20B05 Let $G_{1}$, $G_{2}$, ... be a sequence of groups each of which is either an alternating group, a symmetric group or a cyclic group and construct a sequence $(W_{i})$ of wreath products via $W_{1} = G_{1}$ and, for each $i \geq 1$, $W_{i+1} = G_{i+1} \operatorname{wr} G_{i}$ via the natural permutation action. We determine the minimum number $d(W_{i})$ of generators required for each wreath product in this sequence. |
| title | Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups |
| topic | Group Theory 20E22 20F05 20D06 20B05 |
| url | https://arxiv.org/abs/2501.17524 |