Geodesic
On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field
Algebra and discrete mathematics, Tome 17 (2014) no. 2, pp. 288-297

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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 product representation we proved that the nilpotency class of $U\!J_2(\mathbb{F}_q)$ 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 $U\!J_n(\mathbb{F}_q)$ is not nilpotent if $n \geq 3$.
Keywords: polynomial ring, unitriangular automorphism, finite field, wreath product, nilpotent group, central series. 
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     author = {Yuriy Yu. Leshchenko and Vitaly I. Sushchansky},
     title = {On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field},
     journal = {Algebra and discrete mathematics},
     pages = {288--297},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2014_17_2_a8/}
}
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Yuriy Yu. Leshchenko; Vitaly I. Sushchansky. On the group of unitriangular automorphisms of the polynomial ring in two variables over a finite field. Algebra and discrete mathematics, Tome 17 (2014) no. 2, pp. 288-297. http://geodesic.mathdoc.fr/item/ADM_2014_17_2_a8/