PreprintCC BY 4.0arXiv
Analogues of Grün's lemma and Baer's theorem for skew left braces
Abstract
We prove in this paper some analogues of the well-known group-theoretical Grün's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theorem, stating that if the quotient by the nth centre of a group is finite, then so is the (n+1)th term of the lower central series, in the scope of infinite skew left braces. These results represent significant improvements over previous work. The trifactorised group associated with a skew left brace will be crucial for our proofs.
Related
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BibTeX
@misc{ballesterbolinches2026analogues,
title = {{Analogues of Grün's lemma and Baer's theorem for skew left braces}},
author = {A. Ballester-Bolinches and R. Esteban-Romero and L. A. Kurdachenko and P. Pérez-Altarriba},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.26286},
eprint = {2606.26286},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26286},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analogues of Grün's lemma and Baer's theorem for skew left braces
AU - A. Ballester-Bolinches
AU - R. Esteban-Romero
AU - L. A. Kurdachenko
AU - P. Pérez-Altarriba
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.26286
UR - https://arxiv.org/abs/2606.26286
AB - We prove in this paper some analogues of the well-known group-theoretical Grün's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theorem, stating that if the quotient by the nth centre of a group is finite, then so is the (n+1)th term of the lower central series, in the scope of infinite skew left braces. These results represent significant improvements over previous work. The trifactorised group associated with a skew left brace will be crucial for our proofs.
ER -