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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2014
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152947 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
|
|---|---|
| ISSN: | 1726-3255 |