On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field

• Date: 2018
• Main Authors: Leshchenko, Yuriy Yu., Sushchansky, Vitaly I.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: polynomial ring; unitriangular automorphism; finite field; wreath product; nilpotent group; central series; 20D15; 20E22; 20E36; 20F14
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1038
• Journal Title: Algebra and Discrete Mathematics

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...