Isomorphism testing of groups of cube-free order

Heiko Dietrich, James B Wilson

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)174-197
Number of pages24
JournalJournal of Algebra
Issue numberSI
Publication statusPublished - 1 Mar 2020


  • Cube-free groups
  • Finite groups
  • Group isomorphisms

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