具有无限平方宽度和消失稳定换位子长度的有限生成无限单群
群论
2010-09-08 v4
摘要
本文证明存在有限生成的无限单群，具有无限换位子宽度和无限平方宽度，且其上不存在稳定无界共轭不变范数，特别地，稳定换位子长度为零。此外，构造了这样一个群的递归表示，其字问题和共轭问题是可判定的。
引用
@article{arxiv.0909.2294,
title = {Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length},
author = {Alexey Muranov},
journal= {arXiv preprint arXiv:0909.2294},
year = {2010}
}
备注
v4: 41 pages, 6 figures rescaled at 120%; references updated, typos corrected, other minor corrections. v3: minor changes to the title, text and figures. v2: 41 pages, 6 figures; correction: Ore's conjecture was proved in 2008; 2 references added. v1: 40 pages, 6 figures