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 |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2022
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1694 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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 \(10p-8\). |
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