Serial group rings of finite groups. \(p\)-solvability
We prove that for any finite \(p\)-solvable group \(G\) with a cyclic \(p\)-Sylow subgroup and any field \(F\) of characteristic \(p\), the group ring \(FG\) is serial. As a corollary for an arbitrary field we will produce a list of all groups of order \(\leq 100\) whose group rings are serial.
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1157 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-11572018-05-16T05:04:06Z Serial group rings of finite groups. \(p\)-solvability Kukharev, Andrei Puninski, Gena Serial ring, group ring, \(p\)-solvable group 20C05,16L30 We prove that for any finite \(p\)-solvable group \(G\) with a cyclic \(p\)-Sylow subgroup and any field \(F\) of characteristic \(p\), the group ring \(FG\) is serial. As a corollary for an arbitrary field we will produce a list of all groups of order \(\leq 100\) whose group rings are serial. Lugansk National Taras Shevchenko University 2018-05-16 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1157 Algebra and Discrete Mathematics; Vol 16, No 2 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1157/649 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-05-16T05:04:06Z |
| collection |
OJS |
| language |
English |
| topic |
Serial ring group ring \(p\)-solvable group 20C05,16L30 |
| spellingShingle |
Serial ring group ring \(p\)-solvable group 20C05,16L30 Kukharev, Andrei Puninski, Gena Serial group rings of finite groups. \(p\)-solvability |
| topic_facet |
Serial ring group ring \(p\)-solvable group 20C05,16L30 |
| format |
Article |
| author |
Kukharev, Andrei Puninski, Gena |
| author_facet |
Kukharev, Andrei Puninski, Gena |
| author_sort |
Kukharev, Andrei |
| title |
Serial group rings of finite groups. \(p\)-solvability |
| title_short |
Serial group rings of finite groups. \(p\)-solvability |
| title_full |
Serial group rings of finite groups. \(p\)-solvability |
| title_fullStr |
Serial group rings of finite groups. \(p\)-solvability |
| title_full_unstemmed |
Serial group rings of finite groups. \(p\)-solvability |
| title_sort |
serial group rings of finite groups. \(p\)-solvability |
| description |
We prove that for any finite \(p\)-solvable group \(G\) with a cyclic \(p\)-Sylow subgroup and any field \(F\) of characteristic \(p\), the group ring \(FG\) is serial. As a corollary for an arbitrary field we will produce a list of all groups of order \(\leq 100\) whose group rings are serial. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1157 |
| work_keys_str_mv |
AT kukharevandrei serialgroupringsoffinitegroupspsolvability AT puninskigena serialgroupringsoffinitegroupspsolvability |
| first_indexed |
2025-07-17T10:36:05Z |
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2025-07-17T10:36:05Z |
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1837890080403881984 |