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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.

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

William L. Paschke (1993)

Mathematica Scandinavica

A one-box-shift morphism between Specht modules.

Künzer, Matthias (2000)

Electronic Research Announcements of the American Mathematical Society [electronic only]

A one-sided Zimin construction.

Cummings, L.J., Mays, M. (2001)

The Electronic Journal of Combinatorics [electronic only]

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

M. D. Pérez-Ramos (1988)

Rendiconti del Seminario Matematico della Università di Padova

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

Gomes, Gracinda M.S., Howie, John M. (1996)

Portugaliae Mathematica

A parallelogram configuration condition in nets

Jitka Markvartová (1993)

Archivum Mathematicum

After describing a (general and special) coordinatization of $k$ -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in $k$ -nets with small degree $k$ .

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