The purpose of this paper is to study the subgroup embedding properties of S-semipermutability, semipermutability, and seminormality. Here we say H is S-semipermutable (resp. semipermutable) in a group Gif H permutes which each Sylow subgroup (resp. subgroup) of G whose order is relatively prime to that of H. We say H is seminormal in a group G if H is normalized by subgroups of G whose order is relatively prime to that of H. In particular, we establish that a seminormal p-subgroup is subnormal. We also establish that the solvable groups in which S-permutability is a transitive relation are precisely the groups in which the subnormal subgroups are all S-semipermutable. Local characterizations of this result are also established.
@article{bwmeta1.element.doi-10_2478_s11533-011-0029-8,
author = {James Beidleman and Mathew Ragland},
title = {Subnormal, permutable, and embedded subgroups in finite groups},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {915-921},
zbl = {1245.20016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0029-8}
}
James Beidleman; Mathew Ragland. Subnormal, permutable, and embedded subgroups in finite groups. Open Mathematics, Tome 9 (2011) pp. 915-921. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0029-8/
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