通过中心化子扩张研究极限群的 pro-p 类似物
群论
2011-07-13 v1
摘要
我们通过中心化子扩张开始研究极限群的一个 pro-p 类似物，并将这类新的 pro-p 群称为 L。我们证明，L 中的 pro-p 群具有有限上同调维数、FP∞ 型以及非正的欧拉示性数。在群论性质方面，证明了它们是自由群与无挠多重 pro-循环群的扩张（free-by-(torsion-free poly-procyclic)），并且如果是非阿贝尔群，则不存在具有无限指数的有限生成非平凡正规子群。此外，还证明了 L 类中的每个 2-生成 pro-p 群要么是自由 pro-p 群，要么是阿贝尔群。
引用
@article{arxiv.1107.2331,
title = {On pro-$p$ analogues of limit groups via extensions of centralizers},
author = {Dessislava H. Kochloukova and Pavel A. Zalesskii},
journal= {arXiv preprint arXiv:1107.2331},
year = {2011}
}
备注
This is a correted version of the paper published in Math. Z. 267 (2011), no. 1-2, 109-128. The difference is Section 4, where we show that the proof of Theorem 4.1 of the published version proves that a pro-p limit group is free-by-(torsion free polyprocyclic). It does not however proves that a pro-p limit group is free-by-(torsion free finitely generated nilpotent)