Infinite dimensional linear groups with many G - invariant subspaces

• Autorzy: Leonid Kurdachenko , Alexey Sadovnichenko , Igor Subbotin
• 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.

Słowa kluczowe

EN

Vector space; Linear groups; Periodic groups; Invariant subspace

Kategorie tematyczne

• 20F16: Solvable groups, supersolvable groups
• 15A03: Vector spaces, linear dependence, rank
• 20F29: Representations of groups as automorphism groups of algebraic systems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 2
• Strony: 261-265

Daty

wydano

2010-04-01

online

2010-04-14

Twórcy

autor

Leonid Kurdachenko

• National University of Dnepropetrovsk

autor

Alexey Sadovnichenko

• National University of Dnepropetrovsk

autor

Igor Subbotin

• National University

Bibliografia

• [1] Baumslag G., Wreath product and p-groups, Proc. Cambridge Philos. Soc, 1959, 55, 224–231 http://dx.doi.org/10.1017/S0305004100033934
• [2] Buckley J.T., Lennox J.C., Neumann B.H., Smith H., Wiegold J., Groups with all subgroups normal-by-finite, Journal Austral. Math. Soc. (Ser. A), 1995, 59, 384–398 http://dx.doi.org/10.1017/S1446788700037289
• [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

Identyfikatory

DOI

10.2478/s11533-010-0010-y