Archiv der Mathematik

, 93:299 | Cite as

Large orbits of elements centralized by a Sylow subgroup

Article

Abstract

If G has a nilpotent normal p-complement and V is a finite, faithful and completely reducible G-module of characteristic p, we prove that there exist \({v_1, v_2 \in V}\) such that \({{\bf C}_{G}{(v_1)}\cap {\bf C}_{G}{(v_2)} = P}\) , where \({P \in {\rm Syl}_p(G)}\) . We hence deduce that, if the normal p-complement K is nontrivial, there exists \({v \in {\bf C}_{V}(P)}\) such that |K : CK(v)|2 > |K|.

Mathematics Subject Classification (2000)

Primary 20D45 Secondary 20D20 

Keywords

Large orbits Normal p-complement Sylow p-subgroups 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Dipartimento di Matematica U. DiniFirenzeItaly
  2. 2.Departament d’ Àlgebra, Facultat de MatemàtiquesUniversitat de ValènciaBurjassot, ValènciaSpain

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