PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2009 | 7 | 2 | 176-185
Tytuł artykułu

On some infinite dimensional linear groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let F be a field, A be a vector space over F, and GL(F,A) 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 dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
2
Strony
176-185
Opis fizyczny
Daty
wydano
2009-06-01
online
2009-05-24
Twórcy
  • Department of Algebra, School of Mathematics and Mechanics, National University of Dnepropetrovsk, Dnepropetrovsk, Ukraine, lkurdachenko@hotmail.com
  • Department of Algebra, School of Mathematics and Mechanics, National University of Dnepropetrovsk, Dnepropetrovsk, Ukraine, asadovnichenko@i.ua
  • Mathematics Department, National University, Los Angeles, USA, isubboti@nu.edu
Bibliografia
  • [1] Buckley J.T., Lennox J.C., Neumann B.H., Smith H., Wiegold J., Groups with all subgroups normal-by-finite, J. Austral. Math. Soc. Ser. A, 1995, 59, 384–398 http://dx.doi.org/10.1017/S1446788700037289[Crossref]
  • [2] 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[WoS][Crossref]
  • [3] Kurdachenko L.A., Muñoz-Escolano J.M., Otal J., Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension, Publ. Mat., 2008, 52, 151–169
  • [4] Kurdachenko L.A., Otal J,. Subbotin I.Ya., Groups with prescribed quotient groups and associated module theory, World Scientific, New Jersey, 2002
  • [5] Kurdachenko L.A, Otal J., Subbotin I.Ya., Artinian modules over group rings, Frontiers in Mathematics, Birkhäuser, Basel, 2007
  • [6] Kurdachenko L.A., Subbotin I.Ya., Linear groups with the maximal condition on subgroups of infinite central dimension, Publ. Mat., 2006, 50, 103–131
  • [7] Muñoz-Escolano J.M., Otal J., Semko N.N., Periodic linear groups with the weak chain conditions on subgroups of infinite central dimension, Comm. Algebra, 2008, 36, 749–763 http://dx.doi.org/10.1080/00927870701724318[WoS][Crossref]
  • [8] Neumann B.H., Groups with finite classes of conjugate subgroups, Math. Z, 1955, 63, 76–96 http://dx.doi.org/10.1007/BF01187925[Crossref]
  • [9] Phillips R.E., Finitary linear groups: a survey, In: Finite and locally finite groups (Istanbul 1994), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 471, Kluwer Acad. Publ., Dordrecht, 1995, 111–146
  • [10] Wehrfritz B.A.F., Infinite linear groups, Springer, Berlin, 1973
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0007-6
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.