New Characterizations of p-Supersolubility of Finite Groups

Abstract

Let H be a subgroup of a finite group G. H is said to be λ-supplemented in G if G has a subgroup T such that G = HT and H ∩ T ≤ H _SE , where H _SE denotes the subgroup of H generated by all those subgroups of H, which are S-quasinormally embedded in G. In this article, some results about the λ-supplemented subgroups are obtained, by which we determine the structure of some classes of finite groups. In particular, some new characterizations of p-supersolubility of finite groups are given under the assumption that some primary subgroups are λ-supplemented. As applications, a number of previous known results are generalized.

Key Words:

• Finite groups
• p-Supersoluble groups
• λ-Supplemented subgroups

2010 Mathematics Subject Classification:

• 20D10
• 20D15
• 20D20
• 20D25

ACKNOWLEDGMENTS

This work was supported by National Natural Science Foundation of China (Grant Nos. 10771172, 11001226) and Postgraduate Innovation Foundation of Southwest University (Grant No. ky2010007) and Natural Science Foundation Project of Chongqing (Grant No. cstc2011jjA00020). The authors would like to express sincere thanks to the referees, whose careful reading and important comments of this article lead to a number of improvements.

Notes

Communicated by V. A. Artamonov.