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Su di un problema combinatorio in teoria dei gruppi

Mario Curzio, Patrizia Longobardi, Mercede Maj (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let G be a group and n an integer ≥ 2 . We say that G has the n -permutation property ( G ∈ P n ) if, for any elements x 1 , x 2 , ⋯ , x n in G , there exists some permutation σ of { 1 , 2 , ⋯ , n } , σ ≠ i ⁢ d . such that x 1 , x 2 , ⋯ , x n = x σ ⁢ ( 1 ) , x σ ⁢ ( 2 ) , ⋯ , x σ ⁢ ( n ) . We prouve that every group G ∈ P n is an FC-nilpotent group of class ≤ n - 1 , and that a finitely generated group has the n -permutation property (for some n ) if, and only if, it is abelian by finite. We prouve also that a group G ∈ P 3 if, and only if, its derived subgroup has order at most 2.

Su una classe di gruppi finiti supersolubili

Alma D’Aniello (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we study the class of finite groups G whose nilpotent residual is a Hall subgroup having all subgroups normal in G .

Subnormal, permutable, and embedded subgroups in finite groups

James Beidleman, Mathew Ragland (2011)

Open Mathematics

The purpose of this paper is to study the subgroup embedding properties of S-semipermutability, semipermutability, and seminormality. Here we say H is S-semipermutable (resp. semipermutable) in a group Gif H permutes which each Sylow subgroup (resp. subgroup) of G whose order is relatively prime to that of H. We say H is seminormal in a group G if H is normalized by subgroups of G whose order is relatively prime to that of H. In particular, we establish that a seminormal p-subgroup is subnormal....

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