Let G be a finite and soluble group factorized by three subgroups A, B and C, that is G= ABC= abc∣ a∈ A, b∈ B, c∈ C , with AB= BA, BC= CB and CA= AC. Let h(G) denote the Fitting length of G. In this paper we prove that if AB and C are nilpotent, then h(G) ≤ h(BC) · h(CA). We also prove that if (| A| , | B|) = 1 and max h(AB) , h(BC) , h(CA) = h, then h(G) ≤ h(h+ 1).
Some results on finite trifactorized groups
Jabara E.
2018-01-01
Abstract
Let G be a finite and soluble group factorized by three subgroups A, B and C, that is G= ABC= abc∣ a∈ A, b∈ B, c∈ C , with AB= BA, BC= CB and CA= AC. Let h(G) denote the Fitting length of G. In this paper we prove that if AB and C are nilpotent, then h(G) ≤ h(BC) · h(CA). We also prove that if (| A| , | B|) = 1 and max h(AB) , h(BC) , h(CA) = h, then h(G) ≤ h(h+ 1).
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