Nilpotent Residual of a Finite Group

2023/05/08 by Eliana Rodrigues, Rodrigues, Eliana, Emerson de Melo +3
Mathematics · Neuroscience · #Finite Group Theory Research #Nuclear Receptors and Signaling

paper · pdf · doi:10.48550/arxiv.2305.04993

Abstract

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 C_G(F) = 1. We prove that the order of γ_∞(G), the rank of γ_∞(G) are bounded in terms of the orders of γ_∞(C_G(H)) and H, the rank of γ_∞(C_G(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⟩.

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