Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.02090 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915976584364032 |
|---|---|
| author | Dantas, Alex Carrazedo de Sousa, Jucélia Ferreira |
| author_facet | Dantas, Alex Carrazedo de Sousa, Jucélia Ferreira |
| contents | 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 $c \leq 2$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02090 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some families of locally graded groups with finitely many orbits under automorphisms Dantas, Alex Carrazedo de Sousa, Jucélia Ferreira Group Theory 20A10, 20E36 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 $c \leq 2$ |
| title | Some families of locally graded groups with finitely many orbits under automorphisms |
| topic | Group Theory 20A10, 20E36 |
| url | https://arxiv.org/abs/2605.02090 |