Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups
We define a wreath product of a Lie algebra \(L\) with the one-dimensional Lie algebra \(L_1\) over \(\mathbb{F}_p\) and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of finite symmetric group \(S_{p^m}\) is isomorphic to the wre...
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| Дата: | 2018 |
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| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/921 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9212018-03-21T07:18:38Z Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups Sushchansky, Vitaly I. Netreba, Nataliya V. Lie algebra, wreath product, semidirect product, Lie algebra associated with the lower central series of the group, Sylow p-subgroup, symmetric group 17B30, 17B60, 20F18, 20F40 We define a wreath product of a Lie algebra \(L\) with the one-dimensional Lie algebra \(L_1\) over \(\mathbb{F}_p\) and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of finite symmetric group \(S_{p^m}\) is isomorphic to the wreath product of \(m\) copies of \(L_1\). As a corollary we describe the Lie algebra associated with Sylow p-subgroup of any symmetric group in terms of wreath product of one-dimensional Lie algebras. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/921 Algebra and Discrete Mathematics; Vol 4, No 1 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/921/450 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-03-21T07:18:38Z |
| collection |
OJS |
| language |
English |
| topic |
Lie algebra wreath product semidirect product Lie algebra associated with the lower central series of the group Sylow p-subgroup symmetric group 17B30 17B60 20F18 20F40 |
| spellingShingle |
Lie algebra wreath product semidirect product Lie algebra associated with the lower central series of the group Sylow p-subgroup symmetric group 17B30 17B60 20F18 20F40 Sushchansky, Vitaly I. Netreba, Nataliya V. Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups |
| topic_facet |
Lie algebra wreath product semidirect product Lie algebra associated with the lower central series of the group Sylow p-subgroup symmetric group 17B30 17B60 20F18 20F40 |
| format |
Article |
| author |
Sushchansky, Vitaly I. Netreba, Nataliya V. |
| author_facet |
Sushchansky, Vitaly I. Netreba, Nataliya V. |
| author_sort |
Sushchansky, Vitaly I. |
| title |
Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups |
| title_short |
Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups |
| title_full |
Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups |
| title_fullStr |
Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups |
| title_full_unstemmed |
Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups |
| title_sort |
wreath product of lie algebras and lie algebras associated with sylow p-subgroups of finite symmetric groups |
| description |
We define a wreath product of a Lie algebra \(L\) with the one-dimensional Lie algebra \(L_1\) over \(\mathbb{F}_p\) and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of finite symmetric group \(S_{p^m}\) is isomorphic to the wreath product of \(m\) copies of \(L_1\). As a corollary we describe the Lie algebra associated with Sylow p-subgroup of any symmetric group in terms of wreath product of one-dimensional Lie algebras. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/921 |
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AT sushchanskyvitalyi wreathproductofliealgebrasandliealgebrasassociatedwithsylowpsubgroupsoffinitesymmetricgroups AT netrebanataliyav wreathproductofliealgebrasandliealgebrasassociatedwithsylowpsubgroupsoffinitesymmetricgroups |
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2025-07-17T10:35:53Z |
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2025-07-17T10:35:53Z |
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1837890067711918080 |