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Abstract
Let σ = {σi ∣ i ∈ I} be a partition of the set of all primes P and G a finite group. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G for some i ∈ I and H contains exactly one Hall σi-subgroup of G for every i such that σi ∩ π(G) ≠ ∅.
Let τH(A) = {σi ∈ σ(G) \ σ(A) ∣ σ(A) ∩ σ(HG) ≠ ∅ for a Hall σi-subgroup H of G}. We say that a subgroup A of G is τσ-permutable or τσ-quasinormal in G with respect to H if AHx = Hx A for all x ∈ G and all H ∈ H such that σ(H) ⊆ τH(A), and τσ-permutable or τσ-quasinormal in G if A is τσ-permutable in G with respect to some complete Hall σ-set of G.
We study G assuming that τσ-quasinormality is a transitive relation in G.
Document Type
Article
Publication Date
9-1-2017
Digital Object Identifier (DOI)
https://doi.org/10.1515/jgth-2017-0016
Repository Citation
Beidleman, James C. and Skiba, Alexander N., "On τσ-Quasinormal Subgroups of Finite Groups" (2017). Mathematics Faculty Publications. 29.
https://uknowledge.uky.edu/math_facpub/29
Notes/Citation Information
Published in Journal of Group Theory, v. 20, issue 5, p. 955-969.
© de Gruyter 2017
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