# Subnormal, permutable, and embedded subgroups in finite groups

James Beidleman; Mathew Ragland

Open Mathematics (2011)

- Volume: 9, Issue: 4, page 915-921
- ISSN: 2391-5455

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topJames Beidleman, and Mathew Ragland. "Subnormal, permutable, and embedded subgroups in finite groups." Open Mathematics 9.4 (2011): 915-921. <http://eudml.org/doc/269184>.

@article{JamesBeidleman2011,

abstract = {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.},

author = {James Beidleman, Mathew Ragland},

journal = {Open Mathematics},

keywords = {Solvable group; PST-group; Subnormal subgroup; S-semipermutable; Seminormal subgroup; finite solvable groups; permutable subgroups; subnormal subgroups; semipermutable subgroups; seminormal subgroups; PST-groups; Sylow subgroups},

language = {eng},

number = {4},

pages = {915-921},

title = {Subnormal, permutable, and embedded subgroups in finite groups},

url = {http://eudml.org/doc/269184},

volume = {9},

year = {2011},

}

TY - JOUR

AU - James Beidleman

AU - Mathew Ragland

TI - Subnormal, permutable, and embedded subgroups in finite groups

JO - Open Mathematics

PY - 2011

VL - 9

IS - 4

SP - 915

EP - 921

AB - 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.

LA - eng

KW - Solvable group; PST-group; Subnormal subgroup; S-semipermutable; Seminormal subgroup; finite solvable groups; permutable subgroups; subnormal subgroups; semipermutable subgroups; seminormal subgroups; PST-groups; Sylow subgroups

UR - http://eudml.org/doc/269184

ER -

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