An automorphism α of the group G is said to be n-unipotent if [g,n α] = 1 for all g ∈ 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.

Some remarks on unipotent automorphisms / Puglisi O.; Traustason G.. - In: INTERNATIONAL JOURNAL OF GROUP THEORY. - ISSN 2251-7650. - STAMPA. - 9:(2020), pp. 293-300. [10.22108/ijgt.2020.119749.1581]

Some remarks on unipotent automorphisms

Puglisi O.
;
Traustason G.
2020

Abstract

An automorphism α of the group G is said to be n-unipotent if [g,n α] = 1 for all g ∈ 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.
2020
9
293
300
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Puglisi O.; Traustason G.
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1206422
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