Year: 2026
Type: preprint
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 $n$th 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.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166076513