大多数有限阶群的多项式时间同构测试
群论
2021-09-03 v4
摘要
[请参阅评论] 我们考虑有限阿贝尔群和有限亚循环群的同构问题。我们证明对于稠密的正整数集合 ，对阶为 的黑盒类型阿贝尔群进行同构测试可在关于 的多项式时间内完成。我们还证明对于给定素因子且稠密的阶 集合，可在关于 的多项式时间内对阶为 的黑盒类型互素亚循环群测试同构。这两类群的先前方法运行时间关于 是指数的。
引用
@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}
}
备注
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