On the F-residual of the direct product of finite groups

被引：0

作者：

Shemetkov, L. A. ^{[1
]}

机构：

[1] Francisk Skorina Gomel State Univ, Phys Mat Sci, Gomel, BELARUS

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2013年 / 19卷 / 03期

关键词：

finite group; direct product; formation; F-residual;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let pi be a subset of the set P of all primes, and let pi ' = P\pi. A formation F is called pi '-saturated if G/O-pi '(phi)(G)) is an element of F implies G is an element of F. If F is a nonempty pi '-saturated formation of pi-soluble groups, then it is proved that (A circle times B)(F) = A(F) circle times B-F for any finite groups A and B. In the case pi = P, this result was proved by K. Doerk and T. Hawkes in 1978.

引用

页码：316 / 320

页数：5