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2009 | 7 | 4 | 650-659
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Permutations which make transitive groups primitive

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive generator each. These primitive groups are certain Mathieu groups, certain projective general and projective special linear groups, and certain subgroups of some affine special linear groups.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
4
Strony
650-659
Opis fizyczny
Daty
wydano
2009-12-01
online
2009-10-31
Twórcy
autor
  • Department of Mathematics, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal, pelopes@math.ist.utl.pt
Bibliografia
  • [1] Alperin J.L., Bell R.B., Groups and representations, Graduate Texts in Mathematics, 162 Springer Verlag, 1995
  • [2] Artin E., The orders of the linear groups, Comm. Pure Appl. Math., 1955, 8, 355–365 http://dx.doi.org/10.1002/cpa.3160080302[Crossref]
  • [3] Bedoya N., Revestimentos ramificados e o problema da decomponibilidade, PhD thesis, Universidade de São Paulo, São Paulo, Brazil, June, 2008 (in Portuguese)
  • [4] Cameron P.J., Permutation groups, London Mathematical Society Student Texts, 45, Cambridge University Press, Cambridge, 1999
  • [5] Conder M., Generating the Mathieu groups and associated Steiner systems, Discrete Math., 1993, 112(1–3), 41–47 http://dx.doi.org/10.1016/0012-365X(93)90222-F[Crossref]
  • [6] Conway J.H., Sloane N.J.A., Sphere packings, lattices and groups, 3rd edition, Grundlehren der Mathematischen Wissenschaften, 290, Springer-Verlag, New York, 1999
  • [7] Dixon J.D., Mortimer B., Permutation groups, Graduate Texts in Mathematics, 163, Springer Verlag, 1996
  • [8] The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.4.10; 2007 (http://www.gap-system.org)
  • [9] Isaacs I.M., Zieschang T., Generating symmetric groups, Am. Math. Monthly, 1995, 102(8), 734–739 http://dx.doi.org/10.2307/2974644[Crossref]
  • [10] Neumann P.M., Primitive permutation groups containing a cycle of prime-power length, Bull. London Math. Soc., 1975, 7, 298–299 http://dx.doi.org/10.1112/blms/7.3.298[Crossref]
  • [11] Wielandt H., Finite permutation groups, Academic Press, New York-London, 1964
  • [12] Zieschang T., Primitive permutation groups containing a p-cycle, Arch. Math., 1995, 64, 471–474 http://dx.doi.org/10.1007/BF01195128[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0050-3
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