6-BFC groups
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.
Bicyclic commutator quotients with one non-elementary component
For any number field with non-elementary -class group , , the punctured capitulation type of in its unramified cyclic cubic extensions , , is an orbit under the action of . By means of Artin’s reciprocity law, the arithmetical invariant is translated to the punctured transfer kernel type of the automorphism group of the second Hilbert -class field of . A classification of finite -groups with low order and bicyclic commutator quotient , , according to the algebraic invariant...
Characterisation of finitely generated soluble finite-by-nilpotent groups
Classification of pro- subgroups of over a -adic ring, where is an odd prime
Connected transversals to subnormal subgroups
Subnormal subgroups possessing connected transversals are briefly discussed.
Der Torsionstyp nilpotenter Gruppen
Die unteren Zentralreihen und Kommutatorreihen spezieller Kongruenzuntergruppen in SL(2,....)
Dimension sugroups of metabelian groups.