On Zappa's question in the case of alternating groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918380890488832 |
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| author | Zhang, Ru Shen, Rulin |
| author_facet | Zhang, Ru Shen, Rulin |
| contents | In 1962, Guido Zappa asked whether a non-trivial coset of a Sylow $p$-subgroup of a finite group could contain only elements whose orders are powers of $p$. Marston Conder gives a positive answer to this question in the case of $p=5$. It is known that the smallest group satisfying the conditions of this problem must be a non-abelian simple group. In this paper, we prove that the smallest group of the Zappa problem could not be an alternating simple group for any prime $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09369 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Zappa's question in the case of alternating groups Zhang, Ru Shen, Rulin Group Theory In 1962, Guido Zappa asked whether a non-trivial coset of a Sylow $p$-subgroup of a finite group could contain only elements whose orders are powers of $p$. Marston Conder gives a positive answer to this question in the case of $p=5$. It is known that the smallest group satisfying the conditions of this problem must be a non-abelian simple group. In this paper, we prove that the smallest group of the Zappa problem could not be an alternating simple group for any prime $p$. |
| title | On Zappa's question in the case of alternating groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2603.09369 |