Nilpotent residual of a finite group

Date

2024-03-01

Author

Rodrigues, Eliana
de Melo, Emerson
Ercan, Gülin

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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〉.

Subject Keywords

Automorphisms, Dihedral groups, Frobenius groups, Frobenius-like groups, Nilpotent residual

URI

https://hdl.handle.net/11511/108184

Collections

Department of Mathematics, Article