Some families of locally graded groups with finitely many orbits under automorphisms

Alex Carrazedo Dantas; Jucélia Ferreira de Sousa

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arXiv · 2605.02090

Some families of locally graded groups with finitely many orbits under automorphisms

Alex Carrazedo Dantas·Jucélia Ferreira de Sousa

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Abstract

In this work, we study three families of locally graded groups with finitely many orbits under automorphisms. We prove that: (i) a residually finite group with finitely many orbits under automorphisms is locally finite and has finite exponent; (ii) a finitely generated locally graded group with finitely many orbits under automorphisms is finite; and (iii) the Mal'cev $\mathbb{Q}$-completion of an $r$-generated free nilpotent group of class $c$ has finitely many orbits under automorphisms if and only if either $r = 2$ and $c = 3$, or $c \leq 2$

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BibTeX RIS

Alex Carrazedo Dantas, Jucélia Ferreira de Sousa. 2026-05-03. Some families of locally graded groups with finitely many orbits under automorphisms. https://arxiv.org/abs/2605.02090

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