|Title:||Virtually nilpotent groups with finitely many orbits under automorphisms|
Dantas, Alex Carrazedo
Melo, Emerson Ferreira de
|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.|
|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.|
|Appears in Collections:||MAT - Artigos publicados em periódicos e preprints|
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