Some remarks on unipotent automorphisms

Orazio Puglisi, Gunnar Traustason

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)293-300
Number of pages8
JournalInternational Journal of Group Theory
Volume9
Issue number4
DOIs
Publication statusPublished - 31 Dec 2020

Keywords

  • Engel element
  • Solvable group
  • Unipotent automorphism

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Some remarks on unipotent automorphisms'. Together they form a unique fingerprint.

Cite this