Polynomial-time isomorphism testing of groups of most finite orders

Heiko Dietrich; James B. Wilson

Polynomial-time isomorphism testing of groups of most finite orders

Group Theory 2021-09-03 v4

Authors: Heiko Dietrich , James B. Wilson

Abstract

[PLEASE SEE COMMENT] We consider the isomorphism problem for finite abelian groups and finite meta-cyclic groups. We prove that for a dense set of positive integers $n$ , isomorphism testing for abelian groups of black-box type of order $n$ can be done in time polynomial in $\log n$ . We also prove that for a dense set of orders $n$ with given prime factors, one can test isomorphism for coprime meta-cyclic groups of black-box type of order $n$ in time polynomial in $\log n$ . Prior methods for these two classes of groups have running times exponential in $\log n$ .

Keywords

isomorphism testing finite abelian groups meta-cyclic groups black-box groups polynomial time dense orders

Cite

@article{arxiv.1806.08872,
  title  = {Polynomial-time isomorphism testing of groups of most finite orders},
  author = {Heiko Dietrich and James B. Wilson},
  journal= {arXiv preprint arXiv:1806.08872},
  year   = {2021}
}

Comments

This draft contains some erroneous statements and some proofs have gaps; please refer to the following publications for corrections. (1) Isomorphism testing of groups of cube-free order. J. Algebra 545 (2020) 174-197. (2) Group isomorphism is nearly-linear time for most orders. FOCS 2021 (accepted, arXiv:2011.03133) (3) The content on groups of black-box type will be revised in a different draft

Polynomial-time isomorphism testing of groups of most finite orders

Abstract

Keywords

Cite

Comments

Related papers