A Characteristic 2-Subgroups of a Finite Special Group.
We prove that if is an integer and is a finitely generated soluble group such that every infinite set of elements of contains a pair which generates a nilpotent subgroup of class at most , then is an extension of a finite group by a torsion-free -Engel group. As a corollary, there exists an integer , depending only on and the derived length of , such that is finite. For , such depends only on .
Let be any group and let be an abelian quasinormal subgroup of . If is any positive integer, either odd or divisible by , then we prove that the subgroup is also quasinormal in .