Authors: N.T. Lupashco
Abstract
Let
![](/files/basm/y2006-n2/y2006-n2-f5.png)
be the multiplication group of a commutative Moufang loop Q. In this paper it is proved that if all infinite abelian subgroups of
![](/files/basm/y2006-n2/y2006-n2-f5.png)
are normal in
![](/files/basm/y2006-n2/y2006-n2-f5.png)
, then Q is associative. If all infinite nonabelian subgroups of
![](/files/basm/y2006-n2/y2006-n2-f5.png)
are normal in
![](/files/basm/y2006-n2/y2006-n2-f5.png)
, then all nonassociative subloops of Q are normal in Q, all nonabelian subgroups of
![](/files/basm/y2006-n2/y2006-n2-f5.png)
are normal in
![](/files/basm/y2006-n2/y2006-n2-f5.png)
and the commutator subgroup
![](/files/basm/y2006-n2/y2006-n2-f5.png)
is a finite 3-group.
Fulltext
![Adobe PDF document](/i/pdf.gif)
–
0.11 Mb