On Normally Embedded Subgroups of Prime Power Order in Finite Groups

Abstract

Let d be the smallest generator number of a finite p-group P and let ℳ _d (P) = {P ₁,…, P _d } be a set of maximal subgroups of P such that . In this article, the structure of a finite group G under some assumptions on the S-quasinormal and normal embedding of subgroups in ℳ _{d p} (G _p ), for each prime p, and Sylow p-subgroups G _p of G is investigated.

Key Words:

• Normally embedded subgroup
• p-Nilpotent group
• Saturated formation
• S-quasinormally embedded subgroup
• Supersolvable group

2000 Mathematics Subject Classification:

• 20D10
• 20D20

ACKNOWLEDGMENT

The authors would like to thank the referee who read the manuscript of this article carefully and contributed a lot of valuable suggestions and useful comments. Indeed, the final corrected version has been finished by the referee by using the Tex file of this article.

Li and He are supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi autonomous region (No. 0249001).

Notes

Communicated by R. Dixon.