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2013 | 11 | 11 | 1914-1922
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Algorithms for permutability in finite groups

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EN
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
Bibliografia
  • [1] Ballester-Bolinches A., Beidleman J.C., Cossey J., Esteban-Romero R., Ragland M.F., Schmidt J., Permutable subnormal subgroups of finite groups, Arch. Math. (Basel), 2009, 92(6), 549–557 http://dx.doi.org/10.1007/s00013-009-2976-x
  • [2] Ballester-Bolinches A., Beidleman J.C., Heineken H., Groups in which Sylow subgroups and subnormal subgroups permute, Illinois J. Math., 2003, 47(1–2), 63–69
  • [3] Ballester-Bolinches A., Beidleman J.C., Heineken H., A local approach to certain classes of finite groups, Comm. Algebra, 2003, 31(12), 5931–5942 http://dx.doi.org/10.1081/AGB-120024860
  • [4] Ballester-Bolinches A., Cosme-Llópez E., Esteban-Romero R., Permut: A GAP4 package to deal with permutability, v. 0.03, available at http://personales.upv.es/_resteban/gap/permut-0.03/
  • [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] Ballester-Bolinches A., Esteban-Romero R., Asaad M., Products of Finite Groups, de Gruyter Exp. Math., 53, Walter de Gruyter, Berlin, 2010 http://dx.doi.org/10.1515/9783110220612
  • [7] Ballester-Bolinches A., Esteban-Romero R., Ragland M., A note on finite PST-groups, J. Group Theory, 2007, 10(2), 205–210 http://dx.doi.org/10.1515/JGT.2007.016
  • [8] Ballester-Bolinches A., Esteban-Romero R., Ragland M., Corrigendum: A note on finite PST-groups, J. Group Theory, 2009, 12(6), 961–963 http://dx.doi.org/10.1515/JGT.2009.026
  • [9] Beidleman J.C., Brewster B., Robinson D.J.S., Criteria for permutability to be transitive in finite groups, J. Algebra, 1999, 222(2), 400–412 http://dx.doi.org/10.1006/jabr.1998.7964
  • [10] 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
  • [11] Huppert B., Endliche Gruppen I, Grundlehren Math. Wiss., 134, Springer, Berlin-Heidelberg-New York, 1967 http://dx.doi.org/10.1007/978-3-642-64981-3
  • [12] Maier R., Schmid P., The embedding of quasinormal subgroups in finite groups, Math. Z., 1973, 131(3), 269–272 http://dx.doi.org/10.1007/BF01187244
  • [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] Schmidt R., Subgroup Lattices of Groups, de Gruyter Exp. Math., 14, Walter de Gruyter, Berlin, 1994 http://dx.doi.org/10.1515/9783110868647
  • [16] The GAP Group, GAP - Groups, Algorithms, Programming, v. 4.5.7, 2012
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0299-4
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