On the order of transitive permutation groups with cyclic point-stabilizer

Andrea Lucchini

Displaying similar documents to “On the order of transitive permutation groups with cyclic point-stabilizer”

On $S$ -quasinormal and $c$ -normal subgroups of a finite group

Shirong Li, Yangming Li (2008)

Czechoslovak Mathematical Journal

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Let $ℱ$ be a saturated formation containing the class of supersolvable groups and let $G$ be a finite group. The following theorems are presented: (1) $G \in ℱ$ if and only if there is a normal subgroup $H$ such that $G / H \in ℱ$ and every maximal subgroup of all Sylow subgroups of $H$ is either $c$ -normal or $S$ -quasinormally embedded in $G$ . (2) $G \in ℱ$ if and only if there is a normal subgroup $H$ such that $G / H \in ℱ$ and every maximal subgroup of all Sylow subgroups of $F^{*} (H)$ , the generalized Fitting subgroup of $H$ , is either $c$ -normal...

Cyclic and dihedral constructions of even order

Aleš Drápal (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let $G (\circ)$ and $G (*)$ be two groups of finite order $n$ , and suppose that they share a normal subgroup $S$ such that $u \circ v = u * v$ if $u \in S$ or $v \in S$ . Cases when $G / S$ is cyclic or dihedral and when $u \circ v \neq u * v$ for exactly $n^{2} / 4$ pairs $(u, v) \in G \times G$ have been shown to be of crucial importance when studying pairs of 2-groups with the latter property. In such cases one can describe two general constructions how to get all possible $G (*)$ from a given $G = G (\circ)$ . The constructions, denoted by $G [α, h]$ and $G [β, γ, h]$ , respectively, depend on a coset $α$ (or two cosets $β$ and $γ$ ) modulo...

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

Qingjun Kong, Qingfeng Liu (2014)

Czechoslovak Mathematical Journal

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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.

Finite groups in which $τ$ -quasinormality is a transitive relation

Vladimir O. Lukyanenko, Alexander N. Skiba (2010)

Rendiconti del Seminario Matematico della Università di Padova

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Displaying similar documents to “On the order of transitive permutation groups with cyclic point-stabilizer”

On S -quasinormal and c -normal subgroups of a finite group

Cyclic and dihedral constructions of even order

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

Finite groups in which τ -quasinormality is a transitive relation

On $S$ -quasinormal and $c$ -normal subgroups of a finite group

Finite groups in which $τ$ -quasinormality is a transitive relation