On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field
The group UJ₂(Fq) of unitriangular automorphisms of the polynomial ring in two variables over a finite field Fq, q = pm, is studied. We proved that UJ₂(Fq) is isomorphic to a standard wreath product of elementary Abelian p-groups. Using wreath product representation we proved that the nilpotency cla...
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| Видавець: | Інститут прикладної математики і механіки НАН України |
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| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2014
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152947 |
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| Цитувати: | On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field / Yu. Leshchenko, V. Sushchansky // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 288–297. — Бібліогр.: 7 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | The group UJ₂(Fq) of unitriangular automorphisms of the polynomial ring in two variables over a finite field Fq, q = pm, is studied. We proved that UJ₂(Fq) is isomorphic to a standard wreath product of elementary Abelian p-groups. Using wreath product representation we proved that the nilpotency class of UJ₂(Fq) 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 UJn(Fq) is not nilpotent if n ≥ 3. |
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