Let G be a solvable group and H a solvable subgroup of Aut(G) whose elements are n-unipotent. When H is finitely generated, we show that it stabilizes a finite series in G and conclude that H is nilpotent. If G furthermore has a characteristic series with torsion-free factors. the same conclusion as above holds without the extra assumption that H is finitely generated.
Unipotent automorphisms of solvable groups / Puglisi, Orazio; Traustason, Gunnar. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - STAMPA. - 20:(2017), pp. 573-578. [10.1515/jgth-2016-0049]
Unipotent automorphisms of solvable groups
PUGLISI, ORAZIO;TRAUSTASON, GUNNAR
2017
Abstract
Let G be a solvable group and H a solvable subgroup of Aut(G) whose elements are n-unipotent. When H is finitely generated, we show that it stabilizes a finite series in G and conclude that H is nilpotent. If G furthermore has a characteristic series with torsion-free factors. the same conclusion as above holds without the extra assumption that H is finitely generated.File in questo prodotto:
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