A class of generalized supersoluble groups.
A generalization of a theorem of A. D. Otto.
A Magnus-Witt type isomorphism for non-free groups.
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 .
A note on groups with hamiltonian quotients
A note on groups with torsion-free abelianization and trivial multiplicator.
A note on the Jordan-Hölder theorem
A proof of Ph. Hall's theorem on dimension subgroups
A radical for free groups
Abelian quasinormal subgroups of groups
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 .
Almost fixed-point-free automorphisms of prime order
Let ϕ be an automorphism of prime order p of the group G with C G(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived length are...
An analytic interpretation of real dimension subgroups.