Dual-standard subgroups in nonperiodic locally soluble groups

Stewart E. Stonehewer; Giovanni Zacher

Displaying similar documents to “Dual-standard subgroups in nonperiodic locally soluble groups”

Some lattice properties of normal-by-finite subgroups

Maria De Falco, Carmela Musella (2003)

Bollettino dell'Unione Matematica Italiana

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A subgroup $H$ of a group $G$ is said to be normal-by-finite if the core $H_{G}$ of $H$ in $G$ has finite index in $H$ . It has been proved by Buckley, Lennox, Neumann, Smith and Wiegold that if every subgroup of a group G is normal-by-finite, then $G$ is abelian-by-finite, provided that all its periodic homomorphic images are locally finite. The aim of this article is to describe the structure of groups G for which the partially ordered set $nf (G)$ consisting of all normal-by-finite subgroups satisfies certain...

Groups whose all subgroups are ascendant or self-normalizing

Leonid Kurdachenko, Javier Otal, Alessio Russo, Giovanni Vincenzi (2011)

Open Mathematics

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This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups,...

On transitivity of pronormality

Leonid A. Kurdachenko, Igor Ya. Subbotin (2002)

Commentationes Mathematicae Universitatis Carolinae

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This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.

On some soluble groups in which $U$ -subgroups form a lattice

Leonid A. Kurdachenko, Igor Ya. Subbotin (2007)

Commentationes Mathematicae Universitatis Carolinae

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The article is dedicated to groups in which the set of abnormal and normal subgroups ( $U$ -subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.

On lattice properties of S-permutably embedded subgroups of finite soluble groups

L. M. Ezquerro, M. Gómez-Fernández, X. Soler-Escrivà (2005)

Bollettino dell'Unione Matematica Italiana

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In this paper we prove the following results. Let π be a set of prime numbers and G a finite π-soluble group. Consider U, V ≤ G and $H \in {Hall}_{π} (G)$ such that $H \cap V \in {Hall}_{π} (V)$ and $1 \neq H \cap U \in {Hall}_{π} (U)$ . Suppose also $H \cap U$ is a Hall π-sub-group of some S-permutable subgroup of G. Then $H \cap U \cap V \in {Hall}_{π} (U \cap V)$ and $〈 H \cap U, H \cap V 〉 \in {Hall}_{π} (〈 U \cap V 〉)$ . Therefore,the set of all S-permutably embedded subgroups of a soluble group G into which a given Hall system Σ reduces is a sublattice of the lattice of all Σ-permutable subgroups of G. Moreover any two subgroups of this sublattice of coprimeorders...

Displaying similar documents to “Dual-standard subgroups in nonperiodic locally soluble groups”

Some lattice properties of normal-by-finite subgroups

Groups whose all subgroups are ascendant or self-normalizing

On transitivity of pronormality

On some soluble groups in which U -subgroups form a lattice

On lattice properties of S-permutably embedded subgroups of finite soluble groups

On some soluble groups in which $U$ -subgroups form a lattice