Adolfo Ballester-Bolinches, James C. Beidleman, Arnold D. Feldman, Matthew F. Ragland
December 9, 2015

### Abstract

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 , U g 〉 𝔉 such that U x = U g . 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.