On the power-commutative kernel of locally nilpotent groups.
Groups in which the bounded nilpotency of two-generator subgroups is a transitive relation.
A nilpotency condition for finitely generated soluble groups
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 .
Page 1