Isomorphism testing of groups of cube-free order

Heiko Dietrich, James B Wilson

Research output: Contribution to journal › Article › Research › peer-review

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 languageEnglish
Number of pages19
JournalJournal of Algebra
DOIs
Publication statusAccepted/In press - 13 Feb 2019

Keywords

  • Cube-free groups
  • Finite groups
  • Group isomorphisms

Cite this

Dietrich, Heiko ; Wilson, James B. / Isomorphism testing of groups of cube-free order. In: Journal of Algebra. 2019.
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Dietrich, H & Wilson, JB 2019, 'Isomorphism testing of groups of cube-free order', Journal of Algebra. https://doi.org/10.1016/j.jalgebra.2019.02.008

Isomorphism testing of groups of cube-free order. / Dietrich, Heiko; Wilson, James B.

In: Journal of Algebra, 13.02.2019.

Research output: Contribution to journal › Article › Research › peer-review

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AB - 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.

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Dietrich H, Wilson JB. Isomorphism testing of groups of cube-free order. Journal of Algebra. 2019 Feb 13. https://doi.org/10.1016/j.jalgebra.2019.02.008

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