New results and old problems in finite transformation groups
New results and old problems in finite transformation groups
复制标题
有限变换群的新结果和老问题
DOI：
10.1090/s0002-9904-1960-10491-0
复制
发表时间：
1960
影响因子：
1.3
通讯作者：
P. A. Smith
中科院分区：
文献类型：
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作者：
P. A. Smith
1.定义.一个变换群（G，X）是由一个群G作用在一个拓扑空间X上形成一个X到自身上的同胚群。在这篇文章中，我将理解G是有限的。对于给定的变换群或“作用”（G，X）和子集HQGy，我们用F（H\ G，X）表示H的不动点集，也就是说，使得hx = x的点x对于hgx是C类的。当i = 0时，我们将放弃X上的流形条件;每个作用都是C°类的。一个可微的行为是一个制定。（G，X）是正交的，如果X是欧氏球面或欧氏空间的开子流形，且trans-
1. Definitions. A transformation group (G, X) consists of a group G acting on a topological space X to form a group of homeomorphisms of X onto itself. I t will be understood throughout this paper that G is finite. For a given transformation group or "action" (G, X) and subset HQGy we denote by F(H\ G, X) the fixed-point set of H—that is, the points x such that hx = x for h gx are of class C. When i = 0 we shall drop the manifold condition on X; every action is then of class C°. A differentiable action is a enaction. (G, X) is orthogonal if X is a euclidean sphere or an open submanifold of a euclidean space and the trans-