2020/09/10 by Viachaslau I. Murashka, Murashka, Viachaslau I., А. Ф. Васильев +1
Computer Science · Engineering · Mathematics · #20D25 (Primary) 20F17 #20F19 (Secondary) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2009.04720
openalex publication_date 2020/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the groups all whose maximal or all Sylow subgroups are K-\mathfrakF-subnormal in their product the with generalizations of the Fitting subgroup F^*(G) and F(G). We prove that a hereditary formation \mathfrakF contains every group all whose Sylow subgroups are K-\mathfrakF-subnormal in their product with F^*(G) if and only if \mathfrakF is the class of all σ-nilpotent groups for some partition σ of the set of all primes. We obtain a new characterization of the σ-nilpotent hypercenter, i.e. the \mathfrakF-hypercenter and the normal largest subgroup which K-\mathfrakF-subnormalize all Sylow subgroups coincide if and only if \mathfrakF is the class of all σ-nilpotent groups.