On Semi Cover-Avoiding Maximal Subgroups of Sylow Subgroups of Finite Groups

Abstract

A subgroup H of a finite group G is called to have semi cover-avoiding property in G if there is a normal series of G such that H either covers or avoids every normal factor of the series. In this article we get some new results under the assumption that every maximal subgroup of Sylow subgroups of a suited subgroup of G has semi cover-avoiding property in G. We state our results in the broader context of formation theory.

Key Words:

• Formation
• Semi cover-avoiding property
• The generalized Fitting subgroup

2000 Mathematics Subject Classification:

• 20D10
• 20D20

ACKNOWLEDGMENT

The authors wish to thank Prof. T. R. Berger for his help. The authors also thank the referee for his or her helpful report.

Project supported in part by NSFC (10871210), TianYuan Fund of Math. of China (10626097) NSF of Guangdong (06023728).

Notes

Communicated by M. R. Dixon.