2023/01/05 by Viachaslau I. Murashka, Murashka, Viachaslau I., А. Ф. Васильев +1
Engineering · Mathematics · #20D25 #20D40 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2301.02199
openalex publication_date 2023/01/05 · openalex created_date 2023/01/08 · openalex updated_date 2026/07/28
The generalized Fitting height h^*(G) of a finite group G is the least number h such that Fh^* (G) = G, where F(0)^* (G) = 1, and F(i+1)^*(G) is the inverse image of the generalized Fitting subgroup F^*(G/F^*(i) (G)). Let p be a prime, 1=G0≤ G1≤…≤ G2h+1=G be the shortest normal series in which for i odd the factor Gi+1/Gi is p-soluble (possibly trivial), and for i even the factor Gi+1/Gi is a (non-empty) direct product of nonabelian simple groups. Then h=λp(G) is called the non-p-soluble length of a group G. We proved that if a finite group G is a mutually permutable product of of subgroups A and B then max\h^*(A), h^*(B)\≤ h^*(G)≤ max\h^*(A), h^*(B)\+1 and max\λp(A), λp(B)\= λp(G). Also we introduced and studied the non-Frattini length.