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...
Збережено в:
| Дата: | 2014 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2014
|
| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152947 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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| id |
irk-123456789-152947 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1529472019-06-14T01:25:01Z On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field Leshchenko, Yu. Sushchansky, V. 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. 2014 Article 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. 1726-3255 2010 MSC:20D15, 20E22, 20E36, 20F14. http://dspace.nbuv.gov.ua/handle/123456789/152947 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Leshchenko, Yu. Sushchansky, V. |
| spellingShingle |
Leshchenko, Yu. Sushchansky, V. On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field Algebra and Discrete Mathematics |
| author_facet |
Leshchenko, Yu. Sushchansky, V. |
| author_sort |
Leshchenko, Yu. |
| title |
On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field |
| title_short |
On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field |
| title_full |
On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field |
| title_fullStr |
On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field |
| title_full_unstemmed |
On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field |
| title_sort |
on the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152947 |
| citation_txt |
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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT leshchenkoyu onthegroupofunitriangularautomorphismsofthepolynomialringintwovariablesoverafinitefield AT sushchanskyv onthegroupofunitriangularautomorphismsofthepolynomialringintwovariablesoverafinitefield |
| first_indexed |
2023-05-20T17:38:28Z |
| last_indexed |
2023-05-20T17:38:28Z |
| _version_ |
1796153758104682496 |