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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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2017 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/156017 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862719940203642880 |
|---|---|
| author | Ercan, G. Güloğlu, İ.Ş. |
| author_facet | Ercan, G. Güloğlu, İ.Ş. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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).
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| first_indexed | 2025-12-07T18:22:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156017 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:22:25Z |
| publishDate | 2017 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Ercan, G. Güloğlu, İ.Ş. 2019-06-17T18:52:50Z 2019-06-17T18:52:50Z 2017 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. https://nasplib.isofts.kiev.ua/handle/123456789/156017 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). This work has been supported by the Research Project TÜBİTAK 114F223. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Finite groups admitting a dihedral group of automorphisms Article published earlier |
| spellingShingle | Finite groups admitting a dihedral group of automorphisms Ercan, G. Güloğlu, İ.Ş. |
| title | 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_short | Finite groups admitting a dihedral group of automorphisms |
| title_sort | finite groups admitting a dihedral group of automorphisms |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156017 |
| work_keys_str_mv | AT ercang finitegroupsadmittingadihedralgroupofautomorphisms AT gulogluis finitegroupsadmittingadihedralgroupofautomorphisms |