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Finitely generated positive cones in Fn × ℤ
Abstract
We construct, for every even n ≥ 2, a positive cone on Fn × ℤ that is finitely generated as a semigroup, extending the previously known construction for n = 2. Malicet, Mann, Rivas and Triestino proved that Fn × ℤ admits an isolated left-order if and only if n is even. Since every finitely generated positive cone determines an isolated left-order, for n ≥ 2, the group Fn × ℤ admits a finitely generated positive cone if and only if n is even.
Related
BibTeX
@misc{su2026finitely,
title = {{Finitely generated positive cones in $F_n \times \mathbbZ$}},
author = {Hang Lu Su},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.31103},
eprint = {2608.31103},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31103},
}
RIS
TY - UNPB
TI - Finitely generated positive cones in F_n × ℤ
AU - Hang Lu Su
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.31103
UR - https://arxiv.org/abs/2608.31103
AB - We construct, for every even n ≥ 2, a positive cone on F_n × ℤ that is finitely generated as a semigroup, extending the previously known construction for n = 2. Malicet, Mann, Rivas and Triestino proved that F_n × ℤ admits an isolated left-order if and only if n is even. Since every finitely generated positive cone determines an isolated left-order, for n ≥ 2, the group F_n × ℤ admits a finitely generated positive cone if and only if n is even.
ER -