Abstract
In this article we study locally nilpotent subgroups of D*: = GL 1(D), where D is a division ring. It is proved that every locally nilpotent subnormal subgroup of D* is central. If D is algebraic over its centre then every locally solvable subnormal subgroup of D* is central. Also, in this case, it is shown that every locally nilpotent maximal subgroup of D* can occur as the multiplicative group of some maximal subfield of D.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENT
The authors thank the referee for his or her comments and suggestions.
Notes
Communicated by M. R. Dixon.