Rendiconti del Seminario Matematico della Università di Padova

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Volume 126, 2011, pp. 229–236
DOI: 10.4171/RSMUP/126-13

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

Karise G. Oliveira[1], Pavel Shumyatsky[2] and Carmela Sica[3]

(1) Instituto Federal de Educação,, Ciência e Tecnologia de Goiás, Av. Universitária s/n, GO 75400-000, Inhumas, Brazil
(2) Departamento de Matemática, Universidade de Brasília, Campus Universitário, DF 70910-900, Brasília, Brazil
(3) Dipartimento di Matematica, Università di Salerno, Via Ponte don Melillo, 84084, Fisciano, Italy

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

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Oliveira Karise, Shumyatsky Pavel, Sica Carmela: On Groups of Odd Order Admitting an Elementary 2-Group of Automorphisms. Rend. Sem. Mat. Univ. Padova 126 (2011), 229-236. doi: 10.4171/RSMUP/126-13