The Herzog-Schönheim conjecture for simple and symmetric groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910190003027968 |
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| author | Garonzi, M. Margolis, L. |
| author_facet | Garonzi, M. Margolis, L. |
| contents | The Herzog-Schönheim conjecture states that if $H_1, \ldots, H_k$ are subgroups of a group $G$ and $x_1, \ldots, x_k$ are elements of $G$ such that $H_1x_1, \ldots, H_kx_k$ is a partition of $G$ into cosets, then two of these subgroups must have the same index. We prove this conjecture for simple groups and for symmetric groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_25118 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Herzog-Schönheim conjecture for simple and symmetric groups Garonzi, M. Margolis, L. Group Theory 20D60, 20B30, 20D05 The Herzog-Schönheim conjecture states that if $H_1, \ldots, H_k$ are subgroups of a group $G$ and $x_1, \ldots, x_k$ are elements of $G$ such that $H_1x_1, \ldots, H_kx_k$ is a partition of $G$ into cosets, then two of these subgroups must have the same index. We prove this conjecture for simple groups and for symmetric groups. |
| title | The Herzog-Schönheim conjecture for simple and symmetric groups |
| topic | Group Theory 20D60, 20B30, 20D05 |
| url | https://arxiv.org/abs/2509.25118 |