EuDML | Browse

A subgroup $H$ of a finite group $G$ is weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G = H K$ . In the paper it is proved that a finite group $G$ is $p$ -nilpotent provided $p$ is the smallest prime number dividing the order of $G$ and every minimal subgroup of $P \cap G^{'}$ is weakly-supplemented in $N_{G} (P),$ where $P$ is a Sylow $p$ -subgroup of $G$ . As applications, some interesting results with weakly-supplemented minimal subgroups of $P \cap G^{'}$ are obtained.

The Join of Two Fitting Classes.

Elspeth Cusack (1979)

Mathematische Zeitschrift

The lattice of Fitting classes which are right extensible by soluble groups.

M.J. Iranzo, Julio P. Lafuente, F. Pérez-Monasor (2005)

Publicacions Matemàtiques

In this paper we study the set of Fitting classes which are right extensible by soluble groups ordered by the inclusion relation. The consideration of the associated lattices gives rise to new Fitting classes and it allows to obtain some injectivity criteria for general Fitting classes.

The lattice of very-well-placed subgroups

Martha Saboyá-Baquero (1996)

Rendiconti del Seminario Matematico della Università di Padova

The $p$ -nilpotency of finite groups with some weakly pronormal subgroups

Jianjun Liu, Jian Chang, Guiyun Chen (2020)

Czechoslovak Mathematical Journal

For a finite group $G$ and a fixed Sylow $p$ -subgroup $P$ of $G$ , Ballester-Bolinches and Guo proved in 2000 that $G$ is $p$ -nilpotent if every element of $P \cap G^{'}$ with order $p$ lies in the center of $N_{G} (P)$ and when $p = 2$ , either every element of $P \cap G^{'}$ with order $4$ lies in the center of $N_{G} (P)$ or $P$ is quaternion-free and $N_{G} (P)$ is $2$ -nilpotent. Asaad introduced weakly pronormal subgroup of $G$ in 2014 and proved that $G$ is $p$ -nilpotent if every element of $P$ with order $p$ is weakly pronormal in $G$ and when $p = 2$ , every element of $P$ with order $4$ is also...

Currently displaying 1 – 18 of 18

Page 1

Displaying 1 – 18 of 18

The Core-Free Groups of Sylow-2-type M24.

The defect groups of a clique, p-solvable groups, and Alperin's conjecture.

The diameter of the character degree graph..

The Euler class and periodicity of group cohomology.

The Fitting Clas ...*.

The Fitting class generated by the $π$ -perfect groups

The formation generated by a finite group

The influence of weakly-supplemented subgroups on the structure of finite groups

The Join of Two Fitting Classes.

The lattice of Fitting classes which are right extensible by soluble groups.

The lattice of very-well-placed subgroups

The $p$ -nilpotency of finite groups with some weakly pronormal subgroups

The $p^{*} p$ -injectors of a finite group

The pi-separability of Certain Factorizable Groups.

The product of generalized subnormal subgroups in finite groups.

Theta pairs and the structure of finite groups.

Three remarks on absolutely solvable groups.

Trace Ideals of Relation Modules of Finite Groups.

Currently displaying 1 – 18 of 18