Large orbits in coprime actions of solvable groups

被引：50

作者：

Dolfi, Silvio ^{[1
]}

机构：

[1] Univ Florence, Dipartimento Matemat, I-50134 Florence, Italy

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 360卷 / 01期

关键词：

finite groups; coprime action; regular orbits;

D O I：

10.1090/S0002-9947-07-04155-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a solvable group of automorphisms of a finite group K. If vertical bar G vertical bar and vertical bar K vertical bar are coprime, then there exists an orbit of G on K of size at least root vertical bar G vertical bar. It is also proved that in a pi-solvable group, the largest normal pi-subgroup is the intersection of at most three Hall pi-subgroups.

引用

页码：135 / 152

页数：18

共 19 条

[1]

DIXON J, 1967, J AUSTR MATH SOC, V7, P419

[2] Intersections of odd order Hall subgroups [J].