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Full-Text Articles in Physical Sciences and Mathematics
Finite Groups In Which Pronomality And 𝔉-Pronormality Coincide, Adolfo Ballester-Bolinches, James C. Beidleman, Arnold D. Feldman, Matthew F. Ragland
Finite Groups In Which Pronomality And 𝔉-Pronormality Coincide, Adolfo Ballester-Bolinches, James C. Beidleman, Arnold D. Feldman, Matthew F. Ragland
Mathematics Faculty Publications
For a formation 𝔉, a subgroup U of a finite group G is said to be 𝔉-pronormal in G if for each g ∈ G, there exists x ∈ ⟨U, Ug⟩ 𝔉 such that Ux = Ug. If 𝔉 contains 𝔑, the formation of nilpotent groups, then every 𝔉-pronormal subgroup is pronormal and, in fact, 𝔑-pronormality is just classical pronormality. The main aim of this paper is to study classes of finite soluble groups in which pronormality and 𝔉-pronormality coincide.