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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/2312.16416 |
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| _version_ | 1866910731772887040 |
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| author | Li, Cai Heng Zhu, Yan Zhou |
| author_facet | Li, Cai Heng Zhu, Yan Zhou |
| contents | Building upon previous results, a classification is given of finite $p$-groups of which subgroups of order $p$ are all fused. This completes the classification problem dated back to Higman 1963 on the so-called Suzuki $2$-groups, and confirms a conjecture of Gross proposed in 1974. As a consequence, two open problems on AT-groups and FIF-groups are solved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16416 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A proof of {Gross}' conjecture on $2$-automorphic $2$-groups Li, Cai Heng Zhu, Yan Zhou Group Theory 20D15, 20D45, 20C33 Building upon previous results, a classification is given of finite $p$-groups of which subgroups of order $p$ are all fused. This completes the classification problem dated back to Higman 1963 on the so-called Suzuki $2$-groups, and confirms a conjecture of Gross proposed in 1974. As a consequence, two open problems on AT-groups and FIF-groups are solved. |
| title | A proof of {Gross}' conjecture on $2$-automorphic $2$-groups |
| topic | Group Theory 20D15, 20D45, 20C33 |
| url | https://arxiv.org/abs/2312.16416 |