研究了群在集合上何时存在不动点的问题

引入了群作用三元组的概念

证明了主要结论:设(X

M

G)为群作用三元组

其中M为非平凡的p-群

p为某个素数

G为p-可解群且在M上的作用不可约.如果CG(M)在X上的作用不传递

则G在X中必有不动点;进而

如果还有CG(M)关键词：Glauberman引理;群作用三元组;不动点;Abstract：The existence problem of fixed-points of groups on sets was studied

the notion of group action triple was introduced

and the main result was proved: Let(X

M

G) be a group action triple

where M is a nontrivial p-group for some prime p

G is p-solvable and acts irreducibly on M

if CG(M) is non-transitive on X

then G has necessarily a fixed-point on X;further

if CG(M)KeyWords：Glauberman lemma;group action triple;fixed point;