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Displaying 161 – 180 of 340

On decomposability of finite groups

Ruifang Chen, Xianhe Zhao (2017)

Czechoslovak Mathematical Journal

Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$ -conjugacy classes, and it is called $n$ -decomposable in $G$ if it is a union of $n$ distinct $G$ -conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained in its...

On dicyclic groups as inner mapping groups of finite loops

Emma Leppälä, Markku Niemenmaa (2016)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be a finite group with a dicyclic subgroup $H$ . We show that if there exist $H$ -connected transversals in $G$ , then $G$ is a solvable group. We apply this result to loop theory and show that if the inner mapping group $I (Q)$ of a finite loop $Q$ is dicyclic, then $Q$ is a solvable loop. We also discuss a more general solvability criterion in the case where $I (Q)$ is a certain type of a direct product.

On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops

Markku Niemenmaa (2018)

Commentationes Mathematicae Universitatis Carolinae

We show that finite commutative inverse property loops may not have nonabelian dihedral 2-groups as their inner mapping group.

On E-S-supplemented subgroups of finite groups

Changwen Li, Xuemei Zhang, Xiaolan Yi (2013)

Colloquium Mathematicae

The major aim of the present paper is to strengthen a nice result of Shemetkov and Skiba which gives some conditions under which every non-Frattini G-chief factor of a normal subgroup E of a finite group G is cyclic. As applications, some recent known results are generalized and unified.

On factorisable soluble groups

Saad Adnan (1990)

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

The intention of this paper is to provide an elementary proof of the following known results: Let G be a finite group of the form G = AB. If A is abelian and B has a nilpotent subgroup of index at most 2, then G is soluble.

On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^{4}$

Markku Niemenmaa (2010)

Commentationes Mathematicae Universitatis Carolinae

We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^{4}$ are centrally nilpotent of class at most two.

On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^{5}$

Markku Niemenmaa (2020)

Commentationes Mathematicae Universitatis Carolinae

We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^{5}$ are centrally nilpotent of class at most two.

On finite groups with independent subgroups.

Zhurtov, A.H., Tsirkhov, A.A. (2010)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

On finite groups with some subgroups of prime indices.

Monakhov, V.S., Tyutyanov, V.N. (2007)

Sibirskij Matematicheskij Zhurnal

On finite loops and their inner mapping groups

Markku Niemenmaa (2004)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider finite loops and discuss the following problem: Which groups are (are not) isomorphic to inner mapping groups of loops? We recall some known results on this problem and as a new result we show that direct products of dihedral 2-groups and nontrivial cyclic groups of odd order are not isomorphic to inner mapping groups of finite loops.

On finite loops whose inner mapping groups have small orders

Markku Niemenmaa (1996)

Commentationes Mathematicae Universitatis Carolinae

We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.

On finite minimal non-p-supersoluble groups

Fernando Tuccillo (1992)

Colloquium Mathematicae

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, V....

On finite soluble groups verifying an extremal condition on subgroups.

Fernando Tuccillo (1991)

Collectanea Mathematica

We classify the finite soluble groups satisfying the following condition: if H is a subgroup of G and H is not nilpotent, then the Fitting subgroup of H is the centralizer in H of its derived subgroup H'.

New criteria of existence and conjugacy of Hall subgroups of finite groups are given.

Currently displaying 161 – 180 of 340

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Displaying 161 – 180 of 340

On decomposability of finite groups

On dicyclic groups as inner mapping groups of finite loops

On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops

On E-S-supplemented subgroups of finite groups

On factorisable soluble groups

On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^{4}$

On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^{5}$

On finite groups with independent subgroups.

On finite groups with some subgroups of prime indices.

On finite loops and their inner mapping groups

On finite loops whose inner mapping groups have small orders

On finite minimal non-p-supersoluble groups

On finite soluble groups verifying an extremal condition on subgroups.

On groups admitting a group of automorphisms whose centralizer has bounded rank.

On groups for which the lattice of normal subgroups is distributive

On groups of odd order admitting an elementary 2-group of automorphisms

On Hall subgroups of a finite group

On Huppert's theorem.

On Internal Formation Theory.

On Kurosh-Amitsur radicals of finite groups.

Currently displaying 161 – 180 of 340