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Algebra and Discrete Mathematics, 2017, том 23, выпуск 2, страницы 223–229
(Mi adm605)
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RESEARCH ARTICLE
Finite groups admitting a dihedral group of automorphisms
Gülin Ercana, İsmail Ş. Güloğlub a Department of Mathematics, Middle East Technical University, Ankara, Turkey
b Department of Mathematics, Doğuş University, Istanbul, Turkey
Аннотация:
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 $C_G(\beta)$.
Ключевые слова:
dihedral group, fixed points, nilpotent length.
Поступила в редакцию: 23.11.2016
Образец цитирования:
Gülin Ercan, İsmail Ş. Güloğlu, “Finite groups admitting a dihedral group of automorphisms”, Algebra Discrete Math., 23:2 (2017), 223–229
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm605 https://www.mathnet.ru/rus/adm/v23/i2/p223
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