@article {
author = {Puglisi, Orazio and Traustason, Gunnar},
title = {Some remarks on unipotent automorphisms},
journal = {International Journal of Group Theory},
volume = {9},
number = {4},
pages = {293-300},
year = {2020},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2020.119749.1581},
abstract = {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.},
keywords = {unipotent automorphism,solvable group,Engel element},
url = {https://ijgt.ui.ac.ir/article_24519.html},
eprint = {https://ijgt.ui.ac.ir/article_24519_ae1db50aa114db6fb769bf2702ed6e0c.pdf}
}