Siblings and twins in finite p-groups and a group identification for the groups of order $2^9$
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| Format: | Preprint |
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2026
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| _version_ | 1866915850147069952 |
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| author | Eick, Bettina Schanze, Henrik |
| author_facet | Eick, Bettina Schanze, Henrik |
| contents | We investigate which invariants of groups are powerful in distinguishing non-isomorphic p-groups. We introduce the notations of siblings and twins for p-groups that are difficult to distinguish and we describe the siblings and twins among the groups of small prime-power order. We then use these ideas to device an effective group identification algorithm for the $10,494,213$ groups of order $2^9$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_09363 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Siblings and twins in finite p-groups and a group identification for the groups of order $2^9$ Eick, Bettina Schanze, Henrik Group Theory 20-08, 20-04, 20D15 We investigate which invariants of groups are powerful in distinguishing non-isomorphic p-groups. We introduce the notations of siblings and twins for p-groups that are difficult to distinguish and we describe the siblings and twins among the groups of small prime-power order. We then use these ideas to device an effective group identification algorithm for the $10,494,213$ groups of order $2^9$. |
| title | Siblings and twins in finite p-groups and a group identification for the groups of order $2^9$ |
| topic | Group Theory 20-08, 20-04, 20D15 |
| url | https://arxiv.org/abs/2603.09363 |