On groups with formational subnormal Sylow subgroups

Abstract

We investigate a finite groupGwith{\mathfrak{F}}-subnormal Sylow subgroups, where{\mathfrak{F}}is a subgroup-closed formation and{\mathfrak{A}_{1}\mathfrak{A}\subseteq\mathfrak{F}\subseteq\mathfrak{N}% \mathcal{A}}. We prove thatGis soluble and the derived subgroup of each metanilpotent subgroup is nilpotent. We also describe the structure of groups in which every Sylow subgroup is{\mathfrak{F}}-subnormal or{\mathfrak{F}}-abnormal.

Formations of Finite Groups in Polynomial Time: $\mathfrak{F}$-residuals and $\mathfrak{F}$-subnormality

“…In [24,25,27,31] groups with K-F-subnormal or F-subnormal Sylow subgroups were studied. The class of all groups with K-F-subnormal (resp.…”

On grouops with formational subnormal or self-normalizing subgroups

“…Groups in which certain subgroups are F-subnormal or self-normalizing were studied in [7]- [9]. In particular, in [9] the structure of group with Fsubnormal or self-normalizing Sylow subgroups was described for the large class of subgroup-closed formations F.…”