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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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2014 |
| ISSN: | 1726-3255 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152947 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862728097918353408 |
|---|---|
| author | Leshchenko, Yu. Sushchansky, V. |
| author_facet | Leshchenko, Yu. Sushchansky, V. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T19:06:45Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-152947 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:06:45Z |
| publishDate | 2014 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Leshchenko, Yu. Sushchansky, V. 2019-06-13T10:53:05Z 2019-06-13T10:53:05Z 2014 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. https://nasplib.isofts.kiev.ua/handle/123456789/152947 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field Article published earlier |
| spellingShingle | On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field Leshchenko, Yu. Sushchansky, V. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152947 |
| work_keys_str_mv | AT leshchenkoyu onthegroupofunitriangularautomorphismsofthepolynomialringintwovariablesoverafinitefield AT sushchanskyv onthegroupofunitriangularautomorphismsofthepolynomialringintwovariablesoverafinitefield |