广义 Burnside 定理
群论
2007-09-17 v2
摘要
所有群都有 2 个生成元。对于每个素数幂 q，广义 Burnside 定理（定理 GB）生成了无限多个可解群。其中一些群（如素数幂指数群）仅包含有限阶元素，因此是有限群；另一些则包含无限阶元素，因而是无限群。所有这些群，即使是无限群，也与指数为 q 的群密切相关。它们至少有一个阶为 q 的生成元，且其换位子群的指数为 q。
引用
@article{arxiv.0709.1688,
title = {The Generalized Burnside Theorem},
author = {S. Bachmuth},
journal= {arXiv preprint arXiv:0709.1688},
year = {2007}
}
评论
7 pages. The only material change from the original version is the abstract. The original abstract is incorrect as stated. The proofs in the original have been left untouched here. We have, however, taken this opportunity to add additional comments in several places and removed an erroneous statement from the introduction as well as the abstract