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2011 | 9 | 4 | 915-921
Tytuł artykułu

Subnormal, permutable, and embedded subgroups in finite groups

Treść / Zawartość
Warianty tytułu
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.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
4
Strony
915-921
Opis fizyczny
Daty
wydano
2011-08-01
online
2011-05-26
Twórcy
Bibliografia
  • [1] Agrawal R.K., Finite groups whose subnormal subgroups permute with all Sylow subgroups, Proc. Amer. Math. Soc., 1975, 47(1), 77–83 http://dx.doi.org/10.1090/S0002-9939-1975-0364444-4
  • [2] Al-Sharo K.A., Beidleman J.C., Heineken H., Ragland M.F., Some characterizations of finite groups in which semiper-mutability is a transitive relation, Forum Math., 2010, 22(5), 855–862 http://dx.doi.org/10.1515/FORUM.2010.045
  • [3] Ballester-Bolinches A., Cossey J., Soler-Escrivà X., On a permutability property of subgroups of finite soluble groups, Commun. Contemp. Math., 2010, 12(2), 207–221 http://dx.doi.org/10.1142/S0219199710003798
  • [4] Ballester-Bolinches A., Esteban-Romero R., Sylow permutable subnormal subgroups of finite groups II, Bull. Austr. Math. Soc, 2001, 64(3), 479–486 http://dx.doi.org/10.1017/S0004972700019948
  • [5] Ballester-Bolinches A., Esteban-Romero R., Sylow permutable subnormal subgroups of finite groups, J. Algebra, 2002, 251(2), 727–738 http://dx.doi.org/10.1006/jabr.2001.9138
  • [6] Beidleman J.C., Heineken H., Finite soluble groups whose subnormal subgroups permute with certain classes of subgroups, J. Group Theory, 2003, 6(2), 139–158 http://dx.doi.org/10.1515/jgth.2003.010
  • [7] Beidleman J.C, Heineken H., Pronormal and subnormal subgroups and permutability, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat., 2003, 6(3), 605–615
  • [8] Beidleman J.C, Heineken H., Ragland M.F., Solvable PST-groups, strong Sylow bases and mutually permutable products, J. Algebra, 2009, 321(7), 2022–2027 http://dx.doi.org/10.1016/j.jalgebra.2009.01.007
  • [9] Beidleman J.C, Ragland M.F., The intersection map of subgroups and certain classes of finite groups, Ric. Mat., 2007, 56(2), 217–227 http://dx.doi.org/10.1007/s11587-007-0015-4
  • [10] Kegel O.H., Sylow-Gruppen und Subnormalteiler endlicher Gruppen, Math. Z., 1962, 78, 205–221 http://dx.doi.org/10.1007/BF01195169
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  • [13] Robinson D.J.S., A note on finite groups in which normality is transitive, Proc. Amer. Math. Soc., 1968, 19(4), 933–937 http://dx.doi.org/10.1090/S0002-9939-1968-0230808-9
  • [14] Schmid P., Subgroups permutable with all Sylow subgroups, J. Algebra, 1998, 207(1), 285–293 http://dx.doi.org/10.1006/jabr.1998.7429
  • [15] Wang L, Li Y., Wang Y, Finite groups in which (S-)semipermutability is a transitive relation, Int. J. Algebra, 2008, 2(3) 143–152
  • [16] Zacher G., I gruppi risolubili finiti in cui i sottogruppi di composizione coincidono con i sottogruppi quasi-normali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 1964, 37, 150–154
  • [17] Zhang Q., s-semipermutability and abnormality in finite groups, Comm. Algebra, 1999, 27(9), 4515–4524 http://dx.doi.org/10.1080/00927879908826711
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0029-8
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