Some remarks on unipotent automorphisms
Publish place: International Journal of Group Theory، Vol: 9، Issue: 4
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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JR_THEGR-9-4_006
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
An automorphism $\alpha$ of the group $G$ is said to be $n$-unipotent if $[g,_n\alpha]=۱$ 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.
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Authors
Orazio Puglisi
Dipartimento di Matematica, viale Morgagni ۶۷A
Gunnar Traustason
University of Bath