On finite groups with some conditions on subsets.

Taeri, Bijan

Displaying similar documents to “On finite groups with some conditions on subsets.”

On normal verbal embeddings of some classes of groups.

Mikaelian, Vahagn H. (2004)

Beiträge zur Algebra und Geometrie

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Groups in which the bounded nilpotency of two-generator subgroups is a transitive relation.

Delizia, Costantino, Moravec, Primož, Nicotera, Chiara (2007)

Beiträge zur Algebra und Geometrie

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Sylow 2-subgroups of solvable Q-groups.

Mohammad Reza Darafsheh, H. Sharifi (2007)

Extracta Mathematicae

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A finite group whose irreducible characters are rational valued is called a rational or a Q-group. In this paper we obtain various results concerning the structure of a Sylow 2-subgroup of a solvable Q-group.

Nilpotent Groups

Dailu Li, Xiquan Liang, Yanhong Men (2010)

Formalized Mathematics

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This article describes the concept of the nilpotent group and some properties of the nilpotent groups.

On residually finite groups and their generalizations

Andrzej Strojnowski (1999)

Colloquium Mathematicae

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The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In [2] it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions...

On groups satisfying $| G^{'} {| > [G : Z (G)]}^{1 / 2}$ .

Kaplan, Gil, Lev, Arieh (2006)

Beiträge zur Algebra und Geometrie

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Hyper–(Abelian–by–finite) groups with many subgroups of finite depth

Fares Gherbi, Tarek Rouabhi (2007)

Annales mathématiques Blaise Pascal

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The main result of this note is that a finitely generated hyper-(Abelian-by-finite) group $G$ is finite-by-nilpotent if and only if every infinite subset contains two distinct elements $x$ , $y$ such that $γ_{n} (〈x, x^{y}〉)$ $= γ_{n + 1} (〈x, x^{y}〉)$ for some positive integer $n = n (x, y)$ (respectively, $〈x, x^{y}〉$ is an extension of a group satisfying the minimal condition on normal subgroups by an Engel group).

Properties of subgroups not containing their centralizers

Lemnouar Noui (2009)

Annales mathématiques Blaise Pascal

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In this paper, we give a generalization of Baer Theorem on the injective property of divisible abelian groups. As consequences of the obtained result we find a sufficient condition for a group $G$ to express as semi-direct product of a divisible subgroup $D$ and some subgroup $H$ . We also apply the main Theorem to the $p$ -groups with center of index $p^{2}$ , for some prime $p$ . For these groups we compute $N_{c} (G)$ the number of conjugacy classes and $N_{a}$ the number of abelian maximal subgroups and $N_{n a}$ the number...

On finite minimal non-p-supersoluble groups

Fernando Tuccillo (1992)

Colloquium Mathematicae

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If ℱ is a class of groups, then a minimal non-ℱ-group (a dual minimal non-ℱ-group resp.) is a group which is not in ℱ but any of its proper subgroups (factor groups resp.) is in ℱ. In many problems of classification of groups it is sometimes useful to know structure properties of classes of minimal non-ℱ-groups and dual minimal non-ℱ-groups. In fact, the literature on group theory contains many results directed to classify some of the most remarkable among the aforesaid classes. In particular,...