Finite groups admitting a dihedral group of automorphisms

• Published in: Algebra and Discrete Mathematics
• Date: 2017
• ISSN: 1726-3255
• Main Authors: Ercan, G., Güloğlu, İ.Ş.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/156017
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Finite groups admitting a dihedral group of automorphisms / G. Ercan, İ.Ş. Güloğlu // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 2. — С. 223-229. — Бібліогр.: 17 назв. — англ.

Let D=⟨α,β⟩ be a dihedral group generated by the involutions α and β and let F=⟨αβ⟩. Suppose that D acts on a finite group G by automorphisms in such a way that CG(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 sub...