On Semi-Cover-Avoiding Maximal Subgroups and Solvability of Finite Groups

Abstract

A subgroup H of a finite group G is said to be “semi-cover-avoiding in G” if there is a chief series of G such that H covers or avoids every chief factor of the chief series. In this article, some new characterizations for finite solvable groups are obtained based on the assumption that some subgroups have semi-cover-avoiding properties in the groups.

Key Words:

• Semi-cover-avoiding property
• Soluble groups
• p-singular groups

Mathematics Subject Classification (1991):

• 20D20

ACKNOWLEDGMENTS

The research of Xiuyun Guo was partially supported by a grant of the National Natural Science Foundation of China (10471085); the Shanghai Natural Science Foundation (Grant No. 03ZR); a grant from the Development Foundation of Shanghai Education Committee and a Special Fund for Major Specialities of Shanghai Education Committee.

The research of K. P. Shum was partially supported by a UGC(HK) grant #2160120 (2003/2005).

Notes

Communicated by V. A. Artamonov.