非本原系统的Jordan-Holder定理与有理函数的极大分解
复变函数
2014-02-26 v2 代数几何
群论
摘要
本文证明了关于包含至多两个轨道的循环子群的置换群的非本原系统格的若干结果。作为应用，我们推广了关于多项式函数分解的第一Ritt定理，以及一些其他相关结果。此外，我们讨论了与球面自同构群的有限子群相关的有理函数例子，对于这些例子第一Ritt定理不成立。
引用
@article{arxiv.0712.3869,
title = {Jordan-Holder theorem for imprimitivity systems and maximal decompositions of rational functions},
author = {M. Muzychuk and F. Pakovich},
journal= {arXiv preprint arXiv:0712.3869},
year = {2014}
}
备注
In the current version the approach was considerably simplified and a lot of new material was added (see e.g. Section 2.2, Section 2.3 and Section 3.2). On the other hand, some results of rather calculating character were removed