%0 Journal Article
%T Some remarks on regular subgroups of the affine group
%A M. Chiara Tamburini Bellani
%J International Journal of Group Theory
%D 2012
%I University of Isfahan
%X Let $V$ be a vector space over a field $F$ of characteristic $pgeq 0$ and let $T$ be a regular subgroup of the affine group $AGL(V)$. In the finite dimensional case we show that, if $T$ is abelian or $p>0$, then $T$ is unipotent. For $T$ abelian, pushing forward some ideas used in [A. Caranti, F. Dalla Volta and M. Sala, Abelian regular subgroups of the affine group and radical rings, Publ. Math. Debrecen {bf 69} (2006), 297--308.], we show that the set $left{t-Imid tin Tright}$ is a subalgebra of $End_F(Foplus V)$, which is nilpotent when $V$ has finite dimension. This allows a rather systematic construction of abelian regular subgroups.
%K Affine group
%K Regular subgroups
%U http://www.theoryofgroups.ir/?_action=showPDF&article=468&_ob=1f89ba108eeadac9f94ae6a1a91e8ccc&fileName=full_text.pdf