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Nilpotent residual of a finite group
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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
Journal
Journal of Algebra
DOI
https://doi.org/10.1016/j.jalgebra.2023.11.011
Collections
Department of Mathematics, Article
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BibTeX
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: https://hdl.handle.net/11511/108184.