### 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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Number of pages | 19 |

Journal | Journal of Algebra |

DOIs | |

Publication status | Accepted/In press - 13 Feb 2019 |

### Keywords

- Cube-free groups
- Finite groups
- Group isomorphisms

### Cite this

*Journal of Algebra*. https://doi.org/10.1016/j.jalgebra.2019.02.008

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

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

TY - JOUR

T1 - Isomorphism testing of groups of cube-free order

AU - Dietrich, Heiko

AU - Wilson, James B

PY - 2019/2/13

Y1 - 2019/2/13

N2 - 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.

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.

KW - Cube-free groups

KW - Finite groups

KW - Group isomorphisms

UR - http://www.scopus.com/inward/record.url?scp=85061613975&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2019.02.008

DO - 10.1016/j.jalgebra.2019.02.008

M3 - Article

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -