LocalNR package and some of its applications
In 2024, the authors developed well-known algorithms for the construction and analysis of finite nearrings, implementing it to compute local nearrings of order greater than 31. The new package was named LocalNR package. In this paper, using our method weindicate seventeen \(2\)-generated groups of e...
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| Datum: | 2026 |
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Lugansk National Taras Shevchenko University
2026
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2449 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543061709946880 |
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| author | Raievska, Iryna Raievska, Maryna Sysak, Yaroslav |
| author_facet | Raievska, Iryna Raievska, Maryna Sysak, Yaroslav |
| author_sort | Raievska, Iryna |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2026-01-11T10:11:21Z |
| description | In 2024, the authors developed well-known algorithms for the construction and analysis of finite nearrings, implementing it to compute local nearrings of order greater than 31. The new package was named LocalNR package. In this paper, using our method weindicate seventeen \(2\)-generated groups of exponent 8 which are the additive groups of zero-symmetric local nearrings of order 128; and formulate a conjecture on all such nearrings according to which there left only 2 open cases;prove that there are no local nearrings with the Miller-Moreno multiplicative group of order 64 and the additive group to be a \(2\)-generated group of order 128. |
| first_indexed | 2026-02-08T07:57:15Z |
| format | Article |
| id | admjournalluguniveduua-article-2449 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:15Z |
| publishDate | 2026 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-24492026-01-11T10:11:21Z LocalNR package and some of its applications Raievska, Iryna Raievska, Maryna Sysak, Yaroslav nearring, local nearring, Miller-Moreno group, LocalNR package, GAP 16W30 In 2024, the authors developed well-known algorithms for the construction and analysis of finite nearrings, implementing it to compute local nearrings of order greater than 31. The new package was named LocalNR package. In this paper, using our method weindicate seventeen \(2\)-generated groups of exponent 8 which are the additive groups of zero-symmetric local nearrings of order 128; and formulate a conjecture on all such nearrings according to which there left only 2 open cases;prove that there are no local nearrings with the Miller-Moreno multiplicative group of order 64 and the additive group to be a \(2\)-generated group of order 128. Lugansk National Taras Shevchenko University 2026-01-11 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2449 10.12958/adm2449 Algebra and Discrete Mathematics; Vol 40, No 2 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2449/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2449/1352 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2449/1353 Copyright (c) 2026 Algebra and Discrete Mathematics |
| spellingShingle | nearring local nearring Miller-Moreno group LocalNR package GAP 16W30 Raievska, Iryna Raievska, Maryna Sysak, Yaroslav LocalNR package and some of its applications |
| title | LocalNR package and some of its applications |
| title_full | LocalNR package and some of its applications |
| title_fullStr | LocalNR package and some of its applications |
| title_full_unstemmed | LocalNR package and some of its applications |
| title_short | LocalNR package and some of its applications |
| title_sort | localnr package and some of its applications |
| topic | nearring local nearring Miller-Moreno group LocalNR package GAP 16W30 |
| topic_facet | nearring local nearring Miller-Moreno group LocalNR package GAP 16W30 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2449 |
| work_keys_str_mv | AT raievskairyna localnrpackageandsomeofitsapplications AT raievskamaryna localnrpackageandsomeofitsapplications AT sysakyaroslav localnrpackageandsomeofitsapplications |