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.
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The first author has been supported by the grant MTM2010-19938-C03-01 from MICINN (Spain) and Project of NSFC (11271085).
Ballester-Bolinches, Adolfo; Beidleman, James C.; Feldman, Arnold D.; and Ragland, Matthew F., "Finite Groups in Which Pronomality and 𝔉-Pronormality Coincide" (2015). Mathematics Faculty Publications. 21.