TY - JOUR
ID - 24519
TI - Some remarks on unipotent automorphisms
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Puglisi, Orazio
AU - Traustason, Gunnar
AD - Dipartimento di Matematica, viale Morgagni 67A
AD - University of Bath
Y1 - 2020
PY - 2020
VL - 9
IS - 4
SP - 293
EP - 300
KW - unipotent automorphism
KW - solvable group
KW - Engel element
DO - 10.22108/ijgt.2020.119749.1581
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_24519.html
L1 - https://ijgt.ui.ac.ir/article_24519_ae1db50aa114db6fb769bf2702ed6e0c.pdf
ER -