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  "path": "/abs/2605.26748v1",
  "publishedAt": "2026-05-27T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Saveliy V. Skresanov"
  ],
  "textContent": "**Authors:** Saveliy V. Skresanov\n\nThe 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"
}