JournalsrsmupVol. 126pp. 229–236

On Groups of Odd Order Admitting an Elementary 2-Group of Automorphisms

  • Karise G. Oliveira

    Ciência e Tecnologia de Goiás, Inhumas, Brazil
  • Pavel Shumyatsky

    Universidade de Brasília, Brasilia, Brazil
  • Carmela Sica

    Università di Salerno, Fisciano (Sa), Italy
On Groups of Odd Order Admitting an Elementary 2-Group of Automorphisms cover
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Abstract

Let GG be a finite group of odd order with derived length kk. We show that if GG is acted on by an elementary abelian group AA of order 2n2^n and CG(A)C_G(A) has exponent ee, then GG has a normal series G=G0T0G1T1GnTn=1G=G_0\ge T_0\ge G_1\ge T_1\ge\cdots\ge G_n\ge T_n=1 such that the quotients Gi/TiG_i/T_i have {k,e,n}\{k,e,n\}-bounded exponent and the quotients Ti/Gi+1T_i/G_{i+1} are nilpotent of {k,e,n}\{k,e,n\}-bounded class.

Cite this article

Karise G. Oliveira, Pavel Shumyatsky, Carmela Sica, On Groups of Odd Order Admitting an Elementary 2-Group of Automorphisms. Rend. Sem. Mat. Univ. Padova 126 (2011), pp. 229–236

DOI 10.4171/RSMUP/126-13