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Subnormal, permutable, and embedded subgroups in finite groups

100%

Beidleman J., Ragland M.

Open Mathematics

2011

tom 9

nr 4

915-921

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.

Erratum to: “Subnormal, permutable, and embedded subgroups in finite groups”

100%

Beidleman J., Ragland M.

Open Mathematics

2012

tom 10

nr 2

835-836

The original version of the article was published in Central European Journal of Mathematics, 2011, 9(4), 915–921, DOI: 10.2478/s11533-011-0029-8. Unfortunately, the original version of this article contains a mistake: Lemma 2.1 (2) is not true. We correct Lemma 2.2 (2) and Theorem 1.1 in our paper where this lemma was used.

Ograniczanie wyników

2 Open Mathematics

2 Beidleman J.

2 Ragland M.

1 2012

1 2011

Wyniki wyszukiwania

Subnormal, permutable, and embedded subgroups in finite groups

Erratum to: “Subnormal, permutable, and embedded subgroups in finite groups”