论文标题
置换字符的真实成分
Real Constituents of Permutation Characters
论文作者
论文摘要
我们证明了使用置换字符对W. Burnside定理的广泛概括。在必要的假设下，我们可以对多重性进行一些控制（这是需要有限简单组分类的结果）。一路上，我们还使用该组的奇数真实元素对2封锁定组进行了新的表征。所有这些都可以看作是对Brauer问题11的贡献。我们还获得了2个brauer字符的类似结果。我们还对每个真实元素具有固定点的有限原始置换组进行了分类。
We prove a broad generalization of a theorem of W. Burnside on real characters using permutation characters. Under a necessary hypothesis, We can give some control on multiplicities (a result that needs the Classification of Finite Simple Groups). Along the way, we also give a new characterization of the 2-closed finite groups using odd-order real elements of the group. All this can be seen as a contribution to Brauer's Problem 11. We also obtain similar results for 2-Brauer characters. We also classify finite primitive permutation groups in which every real element has a fixed point.
