Virtually nilpotent groups with finitely many orbits under  automorphisms

Bastos, Raimundo; Dantas, Alex Carrazedo; Melo, Emerson Ferreira de

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Campo DC	Valor	Lengua/Idioma
dc.contributor.author	Bastos, Raimundo	-
dc.contributor.author	Dantas, Alex Carrazedo	-
dc.contributor.author	Melo, Emerson Ferreira de	-
dc.date.accessioned	2021-07-28T02:20:36Z	-
dc.date.available	2021-07-28T02:20:36Z	-
dc.date.issued	2021	-
dc.identifier.citation	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.	pt_BR
dc.identifier.uri	https://repositorio.unb.br/handle/10482/41511	-
dc.language.iso	Inglês	pt_BR
dc.publisher	Springer	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	Virtually nilpotent groups with finitely many orbits under automorphisms	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Extensões	pt_BR
dc.subject.keyword	Automorfismos	pt_BR
dc.subject.keyword	Grupos solúveis	pt_BR
dc.identifier.doi	https://doi.org/10.1007/s00013-020-01566-w	pt_BR
dc.relation.publisherversion	https://link.springer.com/article/10.1007/s00013-020-01566-w	pt_BR
dc.description.abstract1	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.	pt_BR
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