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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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1157 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543334831489024 |
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| author | Kukharev, Andrei Puninski, Gena |
| author_facet | Kukharev, Andrei Puninski, Gena |
| author_sort | Kukharev, Andrei |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-16T05:04:06Z |
| 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. |
| first_indexed | 2026-02-08T08:01:35Z |
| format | Article |
| id | admjournalluguniveduua-article-1157 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:01:35Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | Serial ring group ring \(p\)-solvable group 20C05,16L30 Kukharev, Andrei Puninski, Gena Serial group rings of finite groups. \(p\)-solvability |
| title | 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_short | Serial group rings of finite groups. \(p\)-solvability |
| title_sort | serial group rings of finite groups. \(p\)-solvability |
| topic | Serial ring group ring \(p\)-solvable group 20C05,16L30 |
| topic_facet | Serial ring group ring \(p\)-solvable group 20C05,16L30 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1157 |
| work_keys_str_mv | AT kukharevandrei serialgroupringsoffinitegroupspsolvability AT puninskigena serialgroupringsoffinitegroupspsolvability |