Research Article

On finite Sylow tower and σ-tower groups

Published in: Quaestiones Mathematicae
Volume 46 , issue 9 , 2023 , pages: 1799–1813

DOI: 10.2989/16073606.2022.2120840

Author(s): Jinzhuan Cai Hainan University, P.R. China , Inna N. Safonova Belarusian State University, Belarus , Alexander N. Skiba Francisk Skorina Gomel State University, Belarus , Zhigang Wang Hainan University,

Keywords: 20D10 , 20D15 , 20D20 , 05C25 , Finite group , σ-tower group , Hawkes σ-graph , σ-tower group of type ψ , σ-nilpotent group

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Abstract

In this paper, G is a finite group and σ a partition of the set of all primes ℙ, that is, σ = {σ_i| i ∈ I}, where ℙ = ⋃_i∈I σ_i and σ_i ∩ σ_j = ∅ for all i = j; σ (G) = {σ_i| σ_i ∩ π(G) = ∅}.

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