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A one-sided Auslander--Lyndon theorem
Abstract
We prove that if F is a noncyclic free group, Rtriangleleft F and S≤ F, then the inclusion R'≤ S' implies R≤ S. Thus the normality hypothesis on the second subgroup can be omitted from the Auslander--Lyndon theorem. No restrictions are imposed on ranks or indices.
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BibTeX
@misc{tursunbaev2026onesided,
title = {{A one-sided Auslander--Lyndon theorem}},
author = {Artur Tursunbaev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00804},
eprint = {2610.00804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00804},
}
RIS
TY - UNPB
TI - A one-sided Auslander--Lyndon theorem
AU - Artur Tursunbaev
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00804
UR - https://arxiv.org/abs/2610.00804
AB - We prove that if F is a noncyclic free group, Rtriangleleft F and S≤ F, then the inclusion R'≤ S' implies R≤ S. Thus the normality hypothesis on the second subgroup can be omitted from the Auslander--Lyndon theorem. No restrictions are imposed on ranks or indices.
ER -