Abstract
A group G has cube-free order if no prime to the third power divides |G|. We describe an algorithm that given two cube-free groups G and H of known order, decides whether G≅H, and, if so, constructs an isomorphism G→H. If the groups are input as permutation groups, then our algorithm runs in time polynomial in the input size, improving on the previous super-polynomial bound. An implementation of our algorithm is provided for the computer algebra system GAP.
Original language | English |
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Pages (from-to) | 174-197 |
Number of pages | 24 |
Journal | Journal of Algebra |
Volume | 545 |
Issue number | SI |
DOIs | |
Publication status | Published - 1 Mar 2020 |
Keywords
- Cube-free groups
- Finite groups
- Group isomorphisms