有限单群与局部化
群论
2007-05-23 v2 代数拓扑
摘要
本文旨在同伦理论而来的局部化概念之背景下探讨有限单群中的局部化。我们给出一个有限单群为某单子群的局部化的简易判据,并在多种情形中应用之。迭代此过程使我们能通过局部化序列联结许多单群。我们证明所有散在单群(除可能的 Monster 外)及若干李型群均与交错群相连。有限单群族中是否存在多个连通分支这一问题仍然开放。
引用
@article{arxiv.math/0012217,
title = {Finite simple groups and localization},
author = {Jose L. Rodriguez and Jerome Scherer and Jacques Thevenaz},
journal= {arXiv preprint arXiv:math/0012217},
year = {2007}
}
备注
17 pages. See also http://magma.unil.ch/jscherer/ The two last sections (especially that about preservation of simplicity by localizations) have been removed and will be the subject of a separate paper. Some proofs have been rewritten in a clearer style