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2010 | 8 | 2 | 261-265
Tytuł artykułu

Infinite dimensional linear groups with many G - invariant subspaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
2
Strony
261-265
Opis fizyczny
Daty
wydano
2010-04-01
online
2010-04-14
Twórcy
Bibliografia
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  • [3] Dashkova O.Yu., Dixon M.R., Kurdachenko L.A., Linear groups with rank restrictions on the subgroups of infinite central dimension, Journal Pure and Applied Algebra, 2007, 208, 785–795 http://dx.doi.org/10.1016/j.jpaa.2006.04.002
  • [4] Dixon M.R., Evans M.J., Kurdachenko L.A., Linear groups with the minimal condition on subgroups of infinite central dimension, J. Algebra, 2004, 277, 172–186 http://dx.doi.org/10.1016/j.jalgebra.2004.02.029
  • [5] Dixon M.R., Kurdachenko L.A., Linear groups with infinite central dimension, Groups St Andrews 2005, Vol. 1, London Mathematical Society, Lecture Note Series 339, Cambridge Univ. Press., 2007, 306–312
  • [6] Kurdachenko L.A., Muñoz-Escolano J.M., Otal J., Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension, Publicacions Matemàtiques, 2008, 52(1), 151–169
  • [7] Kurdachenko L.A., Muñoz-Escolano J.M., Otal J., Antifinitary linear groups, Forum Math., 2008, 20(1), 27–44 http://dx.doi.org/10.1515/FORUM.2008.002
  • [8] Kurdachenko L.A., Muñoz-Escolano J.M., Otal J., Semko N.N., Locally nilpotent linear groups with restrictions on their subgroups of infinite central dimension, Geometriae Dedicata, 2009, 138, 69–81 http://dx.doi.org/10.1007/s10711-008-9299-0
  • [9] Kurdachenko L.A., Sadovnichenko A.V., Subbotin I.Ya., On some infinite dimensional groups, Cent. Eur. J. Math., 2009, 7(2), 178–185
  • [10] Kurdachenko L.A., Semko N.N., Subbotin I.Ya., Insight into modules over Dedekind domains, Institute of Mathematics: Kiev-2008
  • [11] Kurdachenko L.A., Subbotin I.Ya., Linear groups with the maximal condition on subgroups of infinite central dimension, Publicacions Matemàtiques, 2006, 50(1), 103–131
  • [12] Muñoz-Escolano J.M., Otal J., Semko N.N., Linear groups with the weak chain conditions on subgroups of infinite central dimension, Comm. Algebra, 2008, 36(2), 749–763 http://dx.doi.org/10.1080/00927870701724318
  • [13] Neumann B.H., Groups with finite classes of conjugate subgroups, Math. Z, 1955, 63, 76–96 http://dx.doi.org/10.1007/BF01187925
  • [14] Phillips R.E., The structure of groups of finitary transformations, J. Algebra, 1988, 119, 400–448 http://dx.doi.org/10.1016/0021-8693(88)90068-3
  • [15] Phillips R.E., Finitary linear groups: a survey, In: Finite and locally finite groups, NATO ASI Series, Vol. 471, Kluver, Dordrecht, 1995, 111–146
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0010-y
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