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On Groups whose Contranormal Subgroups are Normally Complemented

Kurdachenko, L. A., Subbotin, I. Ya. (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 20F16, 20E15.Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.

On hypercentral groups

B. Wehrfritz (2007)

Open Mathematics

Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.

On locally finite minimal non-solvable groups

Ahmet Arıkan, Sezgin Sezer, Howard Smith (2010)

Open Mathematics

In the present work we consider infinite locally finite minimal non-solvable groups, and give certain characterizations. We also define generalizations of the centralizer to establish a result relevant to infinite locally finite minimal non-solvable groups.

On maximal subgroups of minimax groups

Silvana Franciosi, Francesco de Giovanni (1995)

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

It is proved that a soluble residually finite minimax group is finite-by-nilpotent if and only if it has only finitely many maximal subgroups which are not normal.

On minimal non-PC-groups

Francesco Russo, Nadir Trabelsi (2009)

Annales mathématiques Blaise Pascal

A group G is said to be a PC-group, if G / C G ( x G ) is a polycyclic-by-finite group for all x ∈ G . A minimal non-PC-group is a group which is not a PC-group but all of whose proper subgroups are PC-groups. Our main result is that a minimal non-PC-group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.

On non-periodic groups whose finitely generated subgroups are either permutable or pronormal

L. A. Kurdachenko, I. Ya. Subbotin, T. I. Ermolkevich (2013)

Mathematica Bohemica

The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group G is called a generalized radical, if G has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let G be a locally generalized radical...

On semiabelian groups.

Kuzennyi, N.F., Subbotin, I.Ya. (2005)

International Journal of Mathematics and Mathematical Sciences

On some properties of pronormal subgroups

Leonid Kurdachenko, Alexsandr Pypka, Igor Subbotin (2010)

Open Mathematics

New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.

On the Boffa alternative

B. Bajorska, O. Macedońska (2001)

Colloquium Mathematicae

Let G* denote a nonprincipal ultrapower of a group G. In 1986 M.~Boffa posed a question equivalent to the following one: if G does not satisfy a positive law, does G* contain a free nonabelian subsemigroup? We give the affirmative answer to this question in the large class of groups containing all residually finite and all soluble groups, in fact, all groups considered in traditional textbooks on group theory.

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