Título :	Soluble groups with few orbits under automorphisms
Autor :	Bastos Júnior, Raimundo de Araújo Dantas, Alex Carrazedo Melo, Emerson Ferreira de
metadata.dc.identifier.orcid:	https://orcid.org/0000-0002-5733-519X
Assunto::	Extensões Automorfismos Grupos solúveis
Fecha de publicación :	17-mar-2020
Editorial :	Springer
Citación :	BASTOS, Raimundo; DANTAS, Alex C.; MELO, Emerson de. Soluble groups with few orbits under automorphisms. Geometriae Dedicata, v. 209, p. 119-123, 2020. DOI: https://doi.org/10.1007/s10711-020-00525-7. Disponível em: https://link.springer.com/article/10.1007/s10711-020-00525-7.
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). We prove that if G is a soluble group of finite rank such that ω(G)<∞, then G contains a torsion-free radicable nilpotent characteristic subgroup K such that G=K⋊H, where H is a finite group. Moreover, we classify the mixed order soluble groups of finite rank such that ω(G)=3.
DOI:	https://doi.org/10.1007/s10711-020-00525-7
metadata.dc.relation.publisherversion:	https://link.springer.com/article/10.1007/s10711-020-00525-7
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