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Displaying 1 – 20 of 75

On $5$ - and $6$ -decomposable finite groups

Ali Reza Ashrafi, Yao Qing Zhao (2003)

Mathematica Slovaca

On a class of finite solvable groups

James Beidleman, Hermann Heineken, Jack Schmidt (2013)

Open Mathematics

A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group...

On a class of groups with Lagrangian factor groups.

Tuccillo, Fernando (1994)

Portugaliae Mathematica

On a definition for formations

Marco Barlotti (1988)

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

By constructing appropriate faithful simple modules for the group GL(2,3), the author shows that certain "local" definitions for formations are not equivalent.

On a generalization of a theorem of Burnside

Jiangtao Shi (2015)

Czechoslovak Mathematical Journal

A theorem of Burnside asserts that a finite group $G$ is $p$ -nilpotent if for some prime $p$ a Sylow $p$ -subgroup of $G$ lies in the center of its normalizer. In this paper, let $G$ be a finite group and $p$ the smallest prime divisor of $| G |$ , the order of $G$ . Let $P \in {Syl}_{p} (G)$ . As a generalization of Burnside’s theorem, it is shown that if every non-cyclic $p$ -subgroup of $G$ is self-normalizing or normal in $G$ then $G$ is solvable. In particular, if $P ≇ 〈 a, b | a^{p^{n - 1}} = 1, b^{2} = 1, b^{- 1} a b = a^{1 + p^{n - 2}} 〉$ , where $n \geq 3$ for $p > 2$ and $n \geq 4$ for $p = 2$ , then $G$ is $p$ -nilpotent or $p$ -closed.

On a problem of the theory of multiply local formations.

Guo, Wenbin (2004)

Sibirskij Matematicheskij Zhurnal

On a question of Chambers and Makan.

A. Ballester-Bolinches, M. Pérez-Ramos (1996)

Mathematische Zeitschrift

On a theorem of Frobenius.

Bakić, Radoš (1997)

Publications de l'Institut Mathématique. Nouvelle Série

On abelian inner mapping groups of finite loops

Markku Niemenmaa (2000)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.

On complemented subgroups of finite groups

Long Miao (2006)

Czechoslovak Mathematical Journal

A subgroup $H$ of a group $G$ is said to be complemented in $G$ if there exists a subgroup $K$ of $G$ such that $G = H K$ and $H \cap K = 1$ . In this paper we determine the structure of finite groups with some complemented primary subgroups, and obtain some new results about $p$ -nilpotent groups.

On cover-avoiding subgroups of Sylow subgroups of finite groups

Yangming Li (2010)

Rendiconti del Seminario Matematico della Università di Padova

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

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