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Some remarks on unipotent automorphisms | ||
| International Journal of Group Theory | ||
| مقاله 6، دوره 9، شماره 4، اسفند 2020، صفحه 293-300 اصل مقاله (192.84 K) | ||
| نوع مقاله: Proceedings of the conference "Engel conditions in groups" - Bath - UK - 2019 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2020.119749.1581 | ||
| نویسندگان | ||
| Orazio Puglisi* 1؛ Gunnar Traustason2 | ||
| 1Dipartimento di Matematica, viale Morgagni 67A | ||
| 2University of Bath | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| unipotent automorphism؛ solvable group؛ Engel element | ||
| مراجع | ||
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