Geodesic
Finite groups admitting a dihedral group of automorphisms
Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 223-229

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Let $D=\langle \alpha, \beta \rangle$ be a dihedral group generated by the involutions $\alpha$ and $\beta$ and let $F=\langle \alpha \beta \rangle$. Suppose that $D$ acts on a finite group $G$ by automorphisms in such a way that $C_G(F)=1$. In the present paper we prove that the nilpotent length of the group $G$ is equal to the maximum of the nilpotent lengths of the subgroups $C_G(\alpha)$ and $C_G(\beta)$.
Keywords: dihedral group, fixed points, nilpotent length. 
@article{ADM_2017_23_2_a4,
     author = {G\"ulin Ercan and \.Ismail \c{S}. G\"ulo\u{g}lu},
     title = {Finite groups admitting a dihedral group of automorphisms},
     journal = {Algebra and discrete mathematics},
     pages = {223--229},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a4/}
}
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Gülin Ercan; İsmail Ş. Güloğlu. Finite groups admitting a dihedral group of automorphisms. Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 223-229. http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a4/