Subnormal, permutable, and embedded subgroups in finite groups

• Autorzy: James Beidleman , Mathew Ragland
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Solvable group; PST-group; Subnormal subgroup; S-semipermutable; Seminormal subgroup

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 915-921

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

James Beidleman

• University of Kentucky

autor

Mathew Ragland

• Auburn University Montgomery

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0029-8