用元素阶的集合和Sylow子群的正规化子阶的集合刻画奇数维的有限正交单群

摘要

In this article, the author discusses a problem about pure quantitative characterization of some finite simple groups. By means of the classification theorem of finite simple groups and the group structure theorem about the prime graph, it is proved that the finite orthogonal simple group PΩ2N＋1(q) (n ≥ 13) is characterized by its element orders and the orders of normalizers of Sylow subgroups. This result generalizes a conjecture, posed by Shi Wujie , in some sense, that is a finite simple group characterized by its order and the set of its element orders.%本文研究了一类单群的数量刻画问题.运用有限单群分类定理及群的元素阶的素图表示的结构定理,获得了有限群G同构于有限正交单群PΩ2n+1(q)(n≥13),当且仅当群的元素的阶的集合一致和群的Sylow子群的正规化子的阶之集合一致.在某种意义推进施武杰教授的一个猜想.