The Fitting length of a product of mutually permutable finite groups

Let the finite soluble group G=G1G2⋯Gr be the product of pairwise mutually permutable subgroups G1,G2,…,Gr, let h(G) and ℓp(G) be respectively the Fitting length and the p-length of G. The aim of this paper is to prove that h(G)≤max{h(Gi)∣i=1,2,…,r}+1 and ℓp(G)≤max{ℓp(Gi)∣i=1,2,…,r}+1.

Let the finite soluble group G = G(1)G(2) ... Gr be the product of pairwise mutually permutable subgroups G(1), G(2), ... , G(r), let h(G) and l(p)(G) be respectively the Fitting length and the p-length of G. The aim of this paper is to prove that h(G) <= max{h(G(i)) vertical bar i = 1, 2, ... , r} + 1 and l(p)(G) <= max{l(p)(Gi) vertical bar i = 1, 2, ... , r} + 1.