On σ-Permutably Embedded Subgroups of Finite Groups View Full Text


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Article Info

DATE

2019-03

AUTHORS

Chenchen Cao, Li Zhang, Wenbin Guo

ABSTRACT

Let σ = {σi: i ∈ I} be some partition of the set of all primes ℙ, G be a finite group and σ(G) = {σi: σi ∩ π(G)≠Ø}. A set H of subgroups of G is said to be a complete Hall σ-set of G if every non-identity member of H is a Hall σi-subgroup of G and H contains exactly one Hall σi-subgroup of G for every σi ∈ σ(G). G is said to be σ-full if G possesses a complete Hall σ-set. A subgroup H of G is σ-permutable in G if G possesses a complete Hall σ-set H such that HAx= AxH for all A ∈ H and all x ∈ G. A subgroup H of G is σ-permutably embedded in G if H is σ-full and for every σi ∈ σ(H), every Hall σi-subgroup of H is also a Hall σi-subgroup of some σ-permutable subgroup of G. By using the σ-permutably embedded subgroups, we establish some new criteria for a group G to be soluble and supersoluble, and also give the conditions under which a normal subgroup of G is hypercyclically embedded. Some known results are generalized. More... »

PAGES

11-24

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.21136/cmj.2018.0148-17

DOI

http://dx.doi.org/10.21136/cmj.2018.0148-17

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https://app.dimensions.ai/details/publication/pub.1103981161


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