On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field
The group \(U\!J_2(\mathbb{F}_q)\) of unitriangular automorphisms of the polynomial ring in two variables over a finite field \(\mathbb{F}_q\), \(q=p^m\), is studied. We proved that \(U\!J_2(\mathbb{F}_q)\) is isomorphic to a standard wreath product of elementary Abelian \(p\)-groups. Using wreath p...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1038 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | The group \(U\!J_2(\mathbb{F}_q)\) of unitriangular automorphisms of the polynomial ring in two variables over a finite field \(\mathbb{F}_q\), \(q=p^m\), is studied. We proved that \(U\!J_2(\mathbb{F}_q)\) is isomorphic to a standard wreath product of elementary Abelian \(p\)-groups. Using wreath product representation we proved that the nilpotency class of \(U\!J_2(\mathbb{F}_q)\) is \(c=m(p-1)+1\) and the \((k+1)\)th term of the lower central series of this group coincides with the \((c-k)\)th term of its upper central series. Also we showed that \(U\!J_n(\mathbb{F}_q)\) is not nilpotent if \(n \geq 3\). |
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