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.File | Dimensione | Formato | |
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IJGT_2020 _Vol 9_Issue 4_Pages 293-300.pdf
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