141
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

On Hall Normally Embedded Subgroups of Finite Groups

, , &
Pages 3360-3367 | Received 17 Apr 2008, Published online: 22 Sep 2009
 

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.

2000 Mathematics Subject Classification:

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.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.