Título :	Virtually nilpotent groups with finitely many orbits under automorphisms
Autor :	Bastos, Raimundo Dantas, Alex Carrazedo Melo, Emerson Ferreira de
Assunto::	Extensões Automorfismos Grupos solúveis
Fecha de publicación :	2021
Editorial :	Springer
Citación :	BASTOS, Raimundo; DANTAS, Alex C.; MELO, Emerson de. Virtually nilpotent groups with finitely many orbits under automorphisms. Archiv der Mathematik, v. 116, p. 261–270, 2021. DOI: https://doi.org/10.1007/s00013-020-01566-w.
Abstract:	Let G be a group. The orbits of the natural action of Aut(G) on G are called automorphism orbits of G, and the number of automorphism orbits of G is denoted by ω(G). Let G be a virtually nilpotent group such that ω(G)<∞. We prove that G=K⋊H where H is a torsion subgroup and K is a torsion-free nilpotent radicable characteristic subgroup of G. Moreover, we prove that G′=D×Tor(G′) where D is a torsion-free nilpotent radicable characteristic subgroup. In particular, if the maximum normal torsion subgroup τ(G) of G is trivial, then G′ is nilpotent.
DOI:	https://doi.org/10.1007/s00013-020-01566-w
metadata.dc.relation.publisherversion:	https://link.springer.com/article/10.1007/s00013-020-01566-w
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