可解矩阵群与 Burnside 问题
群论
2007-05-23 v1
摘要
所有群均为 2-生成的。对任意素幂 ,定理 1 构造了一个 Laurent 多项式环的商之上的可解矩阵群。如定理 2 与 3 所示,该群与指数为 的群密切相关。第 5 节的定理 4 表明,素幂指数的群包含一个可解群的关系。由此可见指数为 的 Burnside 群是可解的,且易推得这些群的可解类随 趋于无穷。对这项工作至关重要的是关于可解类精确界的早期与 Heilbronn 及 Mochizuki 合写的一篇论文。
引用
@article{arxiv.math/0609415,
title = {Solvable matrix groups and the Burnside problem},
author = {Seymour Bachmuth},
journal= {arXiv preprint arXiv:math/0609415},
year = {2007}
}
备注
14 pages. Section 5, which is 3 pages, has been completely rewritten in an effort to make it simple and clear; no background, only an understanding of the commutative square on page 1 is needed. Sections 2 and 3 are the same as in earlier versions of this article which have been circulating. As these sections are considered correct, the proofs in these sections could be skipped in a first reading if time is a problem. Section 4 is new, but is not needed for section 5