Nilpotent residual of a finite group

Rodrigues, Eliana
de Melo, Emerson
Ercan, Gülin
Let F be a nilpotent group acted on by a group H via automorphisms and let the group G admit the semidirect product FH as a group of automorphisms so that CG(F)=1. We prove that the order of γ∞(G), the rank of γ∞(G) are bounded in terms of the orders of γ∞(CG(H)) and H, the rank of γ∞(CG(H)) and the order of H, respectively in cases where either FH is a Frobenius group; FH is a Frobenius-like group satisfying some certain conditions; or FH=〈α,β〉 is a dihedral group generated by the involutions α and β with F=〈αβ〉 and H=〈α〉.
Journal of Algebra
Citation Formats
E. Rodrigues, E. de Melo, and G. Ercan, “Nilpotent residual of a finite group,” Journal of Algebra, vol. 641, pp. 534–545, 2024, Accessed: 00, 2024. [Online]. Available: