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.
Puglisi, O., Traustason, G. (2020). Some remarks on unipotent automorphisms. International Journal of Group Theory, 9(4), 293-300. doi: 10.22108/ijgt.2020.119749.1581
MLA
Orazio Puglisi; Gunnar Traustason. "Some remarks on unipotent automorphisms". International Journal of Group Theory, 9, 4, 2020, 293-300. doi: 10.22108/ijgt.2020.119749.1581
HARVARD
Puglisi, O., Traustason, G. (2020). 'Some remarks on unipotent automorphisms', International Journal of Group Theory, 9(4), pp. 293-300. doi: 10.22108/ijgt.2020.119749.1581
VANCOUVER
Puglisi, O., Traustason, G. Some remarks on unipotent automorphisms. International Journal of Group Theory, 2020; 9(4): 293-300. doi: 10.22108/ijgt.2020.119749.1581
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