Displaying similar documents to “The influence of weakly-supplemented subgroups on the structure of finite groups”

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...

On weakly s -permutably embedded subgroups

Changwen Li (2011)

Commentationes Mathematicae Universitatis Carolinae

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Suppose G is a finite group and H is a subgroup of G . H is said to be s -permutably embedded in G if for each prime p dividing | H | , a Sylow p -subgroup of H is also a Sylow p -subgroup of some s -permutable subgroup of G ; H is called weakly s -permutably embedded in G if there are a subnormal subgroup T of G and an s -permutably embedded subgroup H s e of G contained in H such that G = H T and H ∩ T ≤ H s e . We investigate the influence of weakly s -permutably embedded subgroups on the p -nilpotency and p -supersolvability...