On the Proof of Some Theorem on Locally Nilpotent Subgroups in Division Rings

Abstract

In Hai and Thin [1], there is a theorem, stating that every locally nilpotent subnormal subgroup in a division ring D is central (see [1, Theoerem 2.2]). Unfortunately, there is some mistake in the proof of this theorem. In this note, we give the another proof of this theorem.

Key Words:

• Central
• Locally nilpotent

2010 Mathematics Subject Classification:

• 16K20

ACKNOWLEDGMENT

The authors thank Mojtaba Ramezannassab for his remarks concerning the proof of our theorem in Hai-Thin [1, Theoerem 2.2]. They are also extremely grateful for the support given by Vietnam National Foundation for Science and Technology Development (NAFOSTED) undergrant 101.01-2011.16.

Notes

Communicated by V. A. Artamonov.