2013/10/28 by Viachaslau I. Murashka, Murashka, V. I., А. Ф. Васильев +1 · 1 citation
Computer Science · Engineering · Mathematics · #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.1310.7445
openalex publication_date 2013/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the Fitting subgroup F(G) of a finite group G and its generalizations: the quasinilpotent radical F^*(G) and the generalized Fitting subgroup F(G) defined by F(G)⊇ Φ(G) and F(G)/Φ(G)=Soc(G/Φ(G)). We sum up known properties of F(G) and suggest some new ones. Let R be a subgroup of a group G. We shall call a subgroup H of G the R-subnormal subgroup if H is subnormal in ⟨ H,R⟩. In this work the influence of R-subnormal subgroups (maximal, Sylow, cyclic primary) on the structure of finite groups are studied in the case when R∈\F(G), F^*(G),F(G)\.