Compact groups with countable Engel sinks
Gorde:
| Egile nagusia: | |
|---|---|
| Argitaratze data: | 2020 |
| Beste egile batzuk: | |
| Formatua: | Article |
| Hizkuntza: | eng |
| Baliabidea: | Repositório Institucional da UnB |
| Download full: | https://repositorio.unb.br/handle/10482/37868 https://doi.org/10.1142/S1664360720500150 |
Gaia: | An Engel sink of an element g of a group G is a set E(g) such that for every x∈G all sufficiently long commutators [...[[x,g],g],…,g] belong to E(g). (Thus, g is an Engel element precisely when we can choose E(g)={1}.) It is proved that if every element of a compact (Hausdorff) group G has a countable (or finite) Engel sink, then G has a finite normal subgroup N such that G/N is locally nilpotent. This settles a question suggested by J. S. Wilson. |