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We prove that if $k > 1$ is an integer and $G$ is a finitely generated soluble group such that every infinite set of elements of $G$ contains a pair which generates a nilpotent subgroup of class at most $k$ , then $G$ is an extension of a finite group by a torsion-free $k$ -Engel group. As a corollary, there exists an integer $n$ , depending only on $k$ and the derived length of $G$ , such that $G / Z_{n} (G)$ is finite. For $k < 4$ , such $n$ depends only on $k$ .

A note on groups with hamiltonian quotients

R. A. Bryce, John Cossey (1998)

Rendiconti del Seminario Matematico della Università di Padova

A note on groups with torsion-free abelianization and trivial multiplicator.

Ralph Strebel (1979)

Commentarii mathematici Helvetici

A note on the Jordan-Hölder theorem

A. Ballester, L. M. Ezquerro (1988)

Rendiconti del Seminario Matematico della Università di Padova

A proof of Ph. Hall's theorem on dimension subgroups

A. Grzegorek (1979)

Colloquium Mathematicae

A radical for free groups

Khambadkone, Meera (1983/1984)

Portugaliae mathematica

Abelian quasinormal subgroups of groups

Stewart E. Stonehewer, Giovanni Zacher (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $G$ be any group and let $A$ be an abelian quasinormal subgroup of $G$ . If $n$ is any positive integer, either odd or divisible by $4$ , then we prove that the subgroup $A^{n}$ is also quasinormal in $G$ .

Almost fixed-point-free automorphisms of prime order

Bertram Wehrfritz (2011)

Open Mathematics

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.

Tasić, Vladimir (1998)

Novi Sad Journal of Mathematics

Bicyclic commutator quotients with one non-elementary component

Daniel Mayer (2023)

Mathematica Bohemica

For any number field $K$ with non-elementary $3$ -class group ${Cl}_{3} (K) ≃ C_{3^{e}} \times C_{3}$ , $e \geq 2$ , the punctured capitulation type $ϰ (K)$ of $K$ in its unramified cyclic cubic extensions $L_{i}$ , $1 \leq i \leq 4$ , is an orbit under the action of $S_{3} \times S_{3}$ . By means of Artin’s reciprocity law, the arithmetical invariant $ϰ (K)$ is translated to the punctured transfer kernel type $ϰ (G_{2})$ of the automorphism group $G_{2} = Gal (F_{3}^{2} (K) / K)$ of the second Hilbert $3$ -class field of $K$ . A classification of finite $3$ -groups $G$ with low order and bicyclic commutator quotient $G / G^{'} ≃ C_{3^{e}} \times C_{3}$ , $2 \leq e \leq 6$ , according to the algebraic invariant...

Subnormal subgroups possessing connected transversals are briefly discussed.

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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

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

Almost fixed-point-free automorphisms of prime order

An analytic interpretation of real dimension subgroups.

Bicyclic commutator quotients with one non-elementary component

Characterisation of finitely generated soluble finite-by-nilpotent groups

Classification of pro- $p$ subgroups of ${SL}_{2}$ over a $p$ -adic ring, where $p$ is an odd prime

Connected transversals to subnormal subgroups

Der Torsionstyp nilpotenter Gruppen

Die unteren Zentralreihen und Kommutatorreihen spezieller Kongruenzuntergruppen in SL(2,....)

Dimension sugroups of metabelian groups.

Currently displaying 1 – 20 of 126