On the units of integral group ring of \(C_{n}\times C_{6}\)
There are many kind of open problems with varying difficulty on units in a given integral group ring. In this note, we characterize the unit group of the integral group ring of \(C_{n}\times C_{6}\) where \(C_{n}=\langle a:a^{n}=1\rangle\) and \(C_{6}=\langle x:x^{6}=1\rangle\). We show that \(\math...
Збережено в:
| Дата: | 2015 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2015
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/104 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-104 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.admjournal.luguniv.edu.ua:article-1042015-11-10T19:25:54Z On the units of integral group ring of \(C_{n}\times C_{6}\) Küsmüş, Ömer group ring, integral group ring, unit group, unit problem 16U60, 16S34 There are many kind of open problems with varying difficulty on units in a given integral group ring. In this note, we characterize the unit group of the integral group ring of \(C_{n}\times C_{6}\) where \(C_{n}=\langle a:a^{n}=1\rangle\) and \(C_{6}=\langle x:x^{6}=1\rangle\). We show that \(\mathcal{U}_{1}(\mathbb{Z}[C_{n}\times C_{6}])\) can be expressed in terms of its 4 subgroups. Furthermore, forms of units in these subgroups are described by the unit group \(\mathcal{U}_{1}(\mathbb{Z}C_{n})\). Notations mostly follow \cite{sehgal2002}. Lugansk National Taras Shevchenko University 2015-11-09 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/104 Algebra and Discrete Mathematics; Vol 20, No 1 (2015): A special issue 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/104/34 Copyright (c) 2015 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
group ring integral group ring unit group unit problem 16U60 16S34 |
| spellingShingle |
group ring integral group ring unit group unit problem 16U60 16S34 Küsmüş, Ömer On the units of integral group ring of \(C_{n}\times C_{6}\) |
| topic_facet |
group ring integral group ring unit group unit problem 16U60 16S34 |
| format |
Article |
| author |
Küsmüş, Ömer |
| author_facet |
Küsmüş, Ömer |
| author_sort |
Küsmüş, Ömer |
| title |
On the units of integral group ring of \(C_{n}\times C_{6}\) |
| title_short |
On the units of integral group ring of \(C_{n}\times C_{6}\) |
| title_full |
On the units of integral group ring of \(C_{n}\times C_{6}\) |
| title_fullStr |
On the units of integral group ring of \(C_{n}\times C_{6}\) |
| title_full_unstemmed |
On the units of integral group ring of \(C_{n}\times C_{6}\) |
| title_sort |
on the units of integral group ring of \(c_{n}\times c_{6}\) |
| description |
There are many kind of open problems with varying difficulty on units in a given integral group ring. In this note, we characterize the unit group of the integral group ring of \(C_{n}\times C_{6}\) where \(C_{n}=\langle a:a^{n}=1\rangle\) and \(C_{6}=\langle x:x^{6}=1\rangle\). We show that \(\mathcal{U}_{1}(\mathbb{Z}[C_{n}\times C_{6}])\) can be expressed in terms of its 4 subgroups. Furthermore, forms of units in these subgroups are described by the unit group \(\mathcal{U}_{1}(\mathbb{Z}C_{n})\). Notations mostly follow \cite{sehgal2002}. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2015 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/104 |
| work_keys_str_mv |
AT kusmusomer ontheunitsofintegralgroupringofcntimesc6 |
| first_indexed |
2024-04-12T06:26:26Z |
| last_indexed |
2024-04-12T06:26:26Z |
| _version_ |
1796109215371100160 |