Finite Groups all of Whose Second Maximal Subgroups are QTI-Subgroups

Abstract

A subgroup H of a finite group G is called a QTI-subgroup if C _G (x) ≤ N _G (H) for any 1 ≠ x ∈ H. In this article, the finite groups all of whose second maximal subgroup are QTI-subgroups are classified.

Key Words:

• Frobenius groups
• QTI-subgroups

2010 Mathematics Subject Classification:

• 20D10
• 20D20

ACKNOWLEDGMENTS

This article is partially supported by the National Natural Science Foundation of China (11071155), SRFDP (200802800011), the Shanghai Leading Academic Discipline Project (J50101).

Notes

Communicated by V. A. Artamonov.