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2013 | 11 | 9 | 1598-1604
Tytuł artykułu

On a class of finite solvable groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
9
Strony
1598-1604
Opis fizyczny
Daty
wydano
2013-09-01
online
2013-06-28
Twórcy
autor
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] Ballester-Bolinches A., Beidleman J., Cossey J., Heineken H., The structure of mutually permutable products of finite nilpotent groups, Internat. J. Algebra Comput., 2007, 17(5-6), 895–904 http://dx.doi.org/10.1142/S0218196707004037
  • [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., Assad M., Products of Finite Groups, de Gruyter Exp. Math., 53, Walter de Gruyter, Berlin, 2010 http://dx.doi.org/10.1515/9783110220612
  • [5] Beidleman J., 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
  • [6] Beidleman J., Heineken H., Groups in which the hypercentral factor group is a T-group, Ric. Mat., 2006, 55(2), 219–225 http://dx.doi.org/10.1007/s11587-006-0012-z
  • [7] Doerk K., Hawkes T.O., Finite Soluble Groups, de Gruyter Exp. Math., 4, Walter de Gruyter, Berlin, 1992 http://dx.doi.org/10.1515/9783110870138
  • [8] Gaschütz W., Gruppen, in denen das Normalteilersein transitiv ist, J. Reine Angew. Math., 1957, 198, 87–92
  • [9] Kegel O.H., Sylow-Gruppen und Subnormalteiler endlicher Gruppen, Math. Z., 1962, 78, 205–221 http://dx.doi.org/10.1007/BF01195169
  • [10] Ragland M.F., Generalizations of groups in which normality is transitive, Comm. Algebra, 2007, 35(10), 3242–3252 http://dx.doi.org/10.1080/00914030701410302
  • [11] Robinson D.J.S., A Course in the Theory of Groups, 2nd ed., Grad. Texts in Math., 80, Springer, New York, 1996 http://dx.doi.org/10.1007/978-1-4419-8594-1
  • [12] van der Waall R.W., Fransman A., On products of groups for which normality is a transitive relation on their Frattini factor groups, Quaestiones Math., 1996(1–2), 19, 59–82 http://dx.doi.org/10.1080/16073606.1996.9631826
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0264-2
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