A note on modular group algebras with upper Lie nilpotency indices
Let \(KG\) be the modular group algebra of an arbitrary group \(G\) over a field \(K\) of characteristic \(p>0\). In this paper we give some improvements of upper Lie nilpotency index \(t^{L}(KG)\) of the group algebra \(KG\). It can be seen that if \(KG\) is Lie nilpotent, then its lower as...
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| Дата: | 2022 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2022
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1694 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-16942022-10-14T16:01:17Z A note on modular group algebras with upper Lie nilpotency indices Bhatt, S. Chandra, H. group algebras, Lie nilpotency index, Lie dimension subgroups 16S34, 17B30 Let \(KG\) be the modular group algebra of an arbitrary group \(G\) over a field \(K\) of characteristic \(p>0\). In this paper we give some improvements of upper Lie nilpotency index \(t^{L}(KG)\) of the group algebra \(KG\). It can be seen that if \(KG\) is Lie nilpotent, then its lower as well as upper Lie nilpotency index is at least \(p+1\). In this way the classification of group algebras \(KG\) with next upper Lie nilpotency index \(t^{L}(KG)\) upto \(9p-7\) have already been classified. Furthermore, we give a complete classification of modular group algebra \(KG\) for which the upper Lie nilpotency index is \(10p-8\). Lugansk National Taras Shevchenko University 2022-10-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1694 10.12958/adm1694 Algebra and Discrete Mathematics; Vol 33, No 2 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1694/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1694/757 Copyright (c) 2022 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
group algebras Lie nilpotency index Lie dimension subgroups 16S34 17B30 |
| spellingShingle |
group algebras Lie nilpotency index Lie dimension subgroups 16S34 17B30 Bhatt, S. Chandra, H. A note on modular group algebras with upper Lie nilpotency indices |
| topic_facet |
group algebras Lie nilpotency index Lie dimension subgroups 16S34 17B30 |
| format |
Article |
| author |
Bhatt, S. Chandra, H. |
| author_facet |
Bhatt, S. Chandra, H. |
| author_sort |
Bhatt, S. |
| title |
A note on modular group algebras with upper Lie nilpotency indices |
| title_short |
A note on modular group algebras with upper Lie nilpotency indices |
| title_full |
A note on modular group algebras with upper Lie nilpotency indices |
| title_fullStr |
A note on modular group algebras with upper Lie nilpotency indices |
| title_full_unstemmed |
A note on modular group algebras with upper Lie nilpotency indices |
| title_sort |
note on modular group algebras with upper lie nilpotency indices |
| description |
Let \(KG\) be the modular group algebra of an arbitrary group \(G\) over a field \(K\) of characteristic \(p>0\). In this paper we give some improvements of upper Lie nilpotency index \(t^{L}(KG)\) of the group algebra \(KG\). It can be seen that if \(KG\) is Lie nilpotent, then its lower as well as upper Lie nilpotency index is at least \(p+1\). In this way the classification of group algebras \(KG\) with next upper Lie nilpotency index \(t^{L}(KG)\) upto \(9p-7\) have already been classified. Furthermore, we give a complete classification of modular group algebra \(KG\) for which the upper Lie nilpotency index is \(10p-8\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2022 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1694 |
| work_keys_str_mv |
AT bhatts anoteonmodulargroupalgebraswithupperlienilpotencyindices AT chandrah anoteonmodulargroupalgebraswithupperlienilpotencyindices AT bhatts noteonmodulargroupalgebraswithupperlienilpotencyindices AT chandrah noteonmodulargroupalgebraswithupperlienilpotencyindices |
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2024-04-12T06:26:45Z |
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2024-04-12T06:26:45Z |
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