Polynomial-time isomorphism test for groups with abelian Sylow subgroups
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917534391861248 |
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| author | Skresanov, Saveliy V. |
| author_facet | Skresanov, Saveliy V. |
| contents | The group isomorphism problem in computational complexity asks whether two finite groups given by their Cayley tables are isomorphic or not. Although polynomial-time isomorphism tests exist for many specific types of groups, no general polynomial-time algorithm is known, classes of solvable and nilpotent groups being the main obstacles. In 2012 Babai and Qiao gave a polynomial-time isomorphism test for the class of solvable groups admitting normal series with abelian Sylow factors. We generalize their result and give a polynomial-time isomorphism test for A-groups, i.e. groups with abelian Sylow subgroups. The algorithm heavily relies both on the computational methods developed by Babai and Qiao, and structural properties of A-groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26748 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomial-time isomorphism test for groups with abelian Sylow subgroups Skresanov, Saveliy V. Group Theory Computational Complexity 20-08 (Primary) 68Q25, 20D20 (Secondary) The group isomorphism problem in computational complexity asks whether two finite groups given by their Cayley tables are isomorphic or not. Although polynomial-time isomorphism tests exist for many specific types of groups, no general polynomial-time algorithm is known, classes of solvable and nilpotent groups being the main obstacles. In 2012 Babai and Qiao gave a polynomial-time isomorphism test for the class of solvable groups admitting normal series with abelian Sylow factors. We generalize their result and give a polynomial-time isomorphism test for A-groups, i.e. groups with abelian Sylow subgroups. The algorithm heavily relies both on the computational methods developed by Babai and Qiao, and structural properties of A-groups. |
| title | Polynomial-time isomorphism test for groups with abelian Sylow subgroups |
| topic | Group Theory Computational Complexity 20-08 (Primary) 68Q25, 20D20 (Secondary) |
| url | https://arxiv.org/abs/2605.26748 |