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Finite groups admitting a dihedral group of automorphisms
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...
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Інститут прикладної математики і механіки НАН України
2017
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/156017 |
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irk-123456789-1560172019-06-18T01:31:08Z Finite groups admitting a dihedral group of automorphisms Ercan, G. Güloğlu, İ.Ş. 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 subgroups CG(α) and CG(β). 2017 Article 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. 1726-3255 2010 MSC:20D10, 20D15, 20D45. http://dspace.nbuv.gov.ua/handle/123456789/156017 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
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 subgroups CG(α) and CG(β). |
| format |
Article |
| author |
Ercan, G. Güloğlu, İ.Ş. |
| spellingShingle |
Ercan, G. Güloğlu, İ.Ş. Finite groups admitting a dihedral group of automorphisms Algebra and Discrete Mathematics |
| author_facet |
Ercan, G. Güloğlu, İ.Ş. |
| author_sort |
Ercan, G. |
| title |
Finite groups admitting a dihedral group of automorphisms |
| title_short |
Finite groups admitting a dihedral group of automorphisms |
| title_full |
Finite groups admitting a dihedral group of automorphisms |
| title_fullStr |
Finite groups admitting a dihedral group of automorphisms |
| title_full_unstemmed |
Finite groups admitting a dihedral group of automorphisms |
| title_sort |
finite groups admitting a dihedral group of automorphisms |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156017 |
| citation_txt |
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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT ercang finitegroupsadmittingadihedralgroupofautomorphisms AT gulogluis finitegroupsadmittingadihedralgroupofautomorphisms |
| first_indexed |
2023-05-20T17:48:42Z |
| last_indexed |
2023-05-20T17:48:42Z |
| _version_ |
1796154141691609088 |