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An order automorphism of a Dlab group not induced by conjugation
Abstract
Let G=D⟨2⟩([0,1]) be equipped with either of its two Dlab orders. There exists an order automorphism α of G such that, for every rank-one subgroup H≤ℝ>0×, every one of the six corresponding Dlab groups A listed below, equipped with any of its linear orders, every order-preserving embedding e:G↪ A, and every u∈ A, there exists f∈ G such that e(α(f))≠ u−1e(f)u.
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BibTeX
@misc{gong2026order,
title = {{An order automorphism of a Dlab group not induced by conjugation}},
author = {Ting Gong and Yong Yang and Michael Ruofan Zeng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18630},
eprint = {2609.18630},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18630},
}
RIS
TY - UNPB
TI - An order automorphism of a Dlab group not induced by conjugation
AU - Ting Gong
AU - Yong Yang
AU - Michael Ruofan Zeng
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18630
UR - https://arxiv.org/abs/2609.18630
AB - Let G=D_⟨2⟩([0,1]) be equipped with either of its two Dlab orders. There exists an order automorphism α of G such that, for every rank-one subgroup H≤ℝ_>0^×, every one of the six corresponding Dlab groups A listed below, equipped with any of its linear orders, every order-preserving embedding e:G↪ A, and every u∈ A, there exists f∈ G such that e(α(f))≠ u^−1e(f)u.
ER -