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Let $H$ be a subgroup of a finite group $G$ . We say that $H$ satisfies the $Π$ -property in $G$ if for any chief factor $L / K$ of $G$ , $| G / K : N_{G / K} (H K / K \cap L / K) |$ is a $π (H K / K \cap L / K)$ -number. We obtain some criteria for the $p$ -supersolubility or $p$ -nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the $Π$ -property.

A note on torsion-by-nilpotent groups

Tarek Rouabhi, Nadir Trabelsi (2007)

Rendiconti del Seminario Matematico della Università di Padova

A Note on two Indices of Semigroup Elements

Vladimir Rakočević (1999)

Publications de l'Institut Mathématique

A note on uniserial loops

Jaroslav Ježek, Tomáš Kepka (2010)

Commentationes Mathematicae Universitatis Carolinae

All ordinal numbers $α$ with the following property are found: there exists a loop such that its subloops form a chain of ordinal type $α$ .

A Note On Units And Divisors Of Zero In Group Rings

N. J. Groenewald, H. J. Schutte (1982)

Publications de l'Institut Mathématique

A note on WA-quasigroups

Tomáš Kepka (1978)

Acta Universitatis Carolinae. Mathematica et Physica

A note on weakly-supplemented subgroups and the solvability of finite groups

Xin Liang, Baiyan Xu (2022)

Czechoslovak Mathematical Journal

Suppose that $G$ is a finite group and $H$ is a subgroup of $G$ . The subgroup $H$ is said to be weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G = H K$ . In this note, by using the weakly-supplemented subgroups, we point out several mistakes in the proof of Theorem 1.2 of Q. Zhou (2019) and give a counterexample.

A note on weakly-supplemented subgroups of finite groups

Hong Pan (2018)

Czechoslovak Mathematical Journal

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, we extend one main result of Kong and Liu (2014).

A number theoretic approach to Sylow r-subgroups of classical groups.

Mashhour I. AlAli, Christoph Hering, Anni Neumann (2005)

Revista Matemática Complutense

The purpose of this paper is to give a general and a simple approach to describe the Sylow r-subgroups of classical groups.

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A note on the splitting length of a finite direct sum of mixed Abelian groups of rank one

A note on the strongly compatible tolerances on an arbitrary semigroup

A Note on the Structure of the Semigroup of Doubly-Stochastic Matrices

A note on the subclass algebra.

A note on the torsion elements in the centralizer of a finite index subgroup.

A note on the WAP-compactification of groups.

A note on the $Π$ -property of some subgroups of finite groups

A note on torsion-by-nilpotent groups

A Note on two Indices of Semigroup Elements

A note on uniserial loops

A Note On Units And Divisors Of Zero In Group Rings

A note on WA-quasigroups

A note on weakly-supplemented subgroups and the solvability of finite groups

A note on weakly-supplemented subgroups of finite groups

A number theoretic approach to Sylow r-subgroups of classical groups.

A numerical invariant for finitely generated groups via actions on graphs.

A one-box-shift morphism between Specht modules.

A one-sided Zimin construction.

A $p$ -stable action of the automorphism group of a group

A $P$ -theorem for inverse semigroups with zero.

Currently displaying 401 – 420 of 984