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 ∈ ℱ if and only if there is a normal subgroup H such that G / H ∈ ℱ and every maximal subgroup of all Sylow subgroups of H is either c -normal or S -quasinormally embedded in G . (2) G ∈ ℱ if and only if there is a normal subgroup H such that G / H ∈ 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 ( ∘ ) and G ( * ) be two groups of finite order n , and suppose that they share a normal subgroup S such that u ∘ v = u * v if u ∈ S or v ∈ S . Cases when G / S is cyclic or dihedral and when u ∘ v ≠ u * v for exactly n 2 / 4 pairs ( u , v ) ∈ G × 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 ( ∘ ) . 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 ∩ 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 ∩ G ' are obtained.