Year: 2026
Type: preprint
Abstract: 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 solvable A-groups, i.e. solvable 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.
Source: arXiv (Cornell University)
Author: Skresanov, Saveliy V.
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3602235587
OpenAlex ID: W7162576286
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