On H σ -permutably embedded subgroups of finite groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 143-158.

Let G be a finite group. Let σ={σ i |iI} be a partition of the set of all primes and n an integer. We write σ(n)={σ i |σ i π(n)}, σ(G)=σ(|G|). A set of subgroups of G is said to be a complete Hall σ-set of G if every member of {1} is a Hall σ i -subgroup of G for some σ i and 𝒸alH contains exact one Hall σ i -subgroup of G for every σ i σ(G). A subgroup A of G is called (i) a σ-Hall subgroup of G if σ(A)σ(|G:A|)=; (ii) σ-permutable in G if G possesses a complete Hall σ-set such that AH x =H x A for all H and all xG. We say that a subgroup A of G is H σ -permutably embedded in G if A is a σ-Hall subgroup of some σ-permutable subgroup of G. We study finite groups G having an H σ -permutably embedded subgroup of order |A| for each subgroup A of G. Some known results are generalized.

Publié le :
DOI : 10.4171/RSMUP/139-4
Classification : 20, 00
Mots clés : Finite group, $\sigma$-Hall subgroup, $\sigma$-subnormal subgroup, $\sigma$-nilpotent group, $H_{\sigma}$-permutably embedded subgroup
Guo, Wenbin 1 ; Zhang, Chi 1 ; Skiba, Alexander 2 ; Sinitsa, D. 2

1 University of Science and Technology of China, Hefei, Anhui, China
2 Francisk Skorina Gomel State University, Gomel, Belarus
@article{RSMUP_2018__139__143_0,
     author = {Guo, Wenbin and Zhang, Chi and Skiba, Alexander and Sinitsa, D.},
     title = {On $H_{\sigma}$-permutably embedded subgroups of finite groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {143--158},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {139},
     year = {2018},
     doi = {10.4171/RSMUP/139-4},
     mrnumber = {3825183},
     zbl = {1483.20031},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/139-4/}
}
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Guo, Wenbin; Zhang, Chi; Skiba, Alexander; Sinitsa, D. On $H_{\sigma}$-permutably embedded subgroups of finite groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 143-158. doi : 10.4171/RSMUP/139-4. http://www.numdam.org/articles/10.4171/RSMUP/139-4/

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