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On the structure of groups whose non-abelian subgroups are subnormal

100%
Kurdachenko L., Atlıhan S., Semko N.
Open Mathematics
|
2014
|
tom 12
|
nr 12
1762-1771
EN
The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.
2
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Subnormal, permutable, and embedded subgroups in finite groups

88%
Beidleman J., Ragland M.
Open Mathematics
|
2011
|
tom 9
|
nr 4
915-921
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.
3
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Erratum to: “Subnormal, permutable, and embedded subgroups in finite groups”

88%
Beidleman J., Ragland M.
Open Mathematics
|
2012
|
tom 10
|
nr 2
835-836
EN
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.
4
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Groups whose all subgroups are ascendant or self-normalizing

63%
Kurdachenko L., Otal J., Russo A., Vincenzi G.
Open Mathematics
|
2011
|
tom 9
|
nr 2
420-432
EN
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1–16].
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