%0 Journal Article
%T Some remarks on unipotent automorphisms
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Puglisi, Orazio
%A Traustason, Gunnar
%D 2020
%\ 12/01/2020
%V 9
%N 4
%P 293-300
%! Some remarks on unipotent automorphisms
%K unipotent automorphism
%K solvable group
%K Engel element
%R 10.22108/ijgt.2020.119749.1581
%X An automorphism $\alpha$ of the group $G$ is said to be $n$-unipotent if $[g,_n\alpha]=1$ for all $g\in G$. In this paper we obtain some results related to nilpotency of groups of $n$-unipotent automorphisms of solvable groups. We also show that, assuming the truth of a conjecture about the representation theory of solvable groups raised by P. Neumann, it is possible to produce, for a suitable prime $p$, an example of a f.g. solvable group possessing a group of $p$-unipotent automorphisms which is isomorphic to an infinite Burnside group. Conversely we show that, if there exists a f.g. solvable group $G$ with a non nilpotent $p$-group $H$ of $n$-automorphisms, then there is such a counterexample where $n$ is a prime power and $H$ has finite exponent.
%U https://ijgt.ui.ac.ir/article_24519_ae1db50aa114db6fb769bf2702ed6e0c.pdf