Abstract
A subgroup H of a finite group G is called Hall normally embedded in G if H is a Hall subgroup of the normal closure H G . Groups which contain a Hall normally embedded subgroup of order d for every factor d of | G | are characterized. Such groups are supersolvable with a cyclic nilpotent residual of square-free order.
ACKNOWLEDGMENTS
The authors are grateful to the referee and the editor, Prof. Dugald Macpherson, who provided their valuable suggestions and helpful comments. In addition, the authors thank the referee who provides his or her detailed reports.
The article was supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi autonomous region (No. 0249001).
Notes
Communicated by D. Macpherson.