上同调维数为3的初等顺从群
群论
2026-05-14 v3
摘要
我们证明了Hirsch长度的无挠初等顺从群是可解的，且其导出长度。该类群包含所有上同调维数为3的可解群。我们还证明了后一子类中的群要么是多项式循环群，要么是半直积，要么是以或为基的真升HNN扩张。
引用
@article{arxiv.2102.02947,
title = {Elementary amenable groups of cohomological dimension 3},
author = {Jonathan A. Hillman},
journal= {arXiv preprint arXiv:2102.02947},
year = {2026}
}
备注
v2: Corollary 7 moved to become new Theorem 5, in \S3. v3: two paragraphs added at end, on realisation by aspherical manifolds