Year: 2026
Type: preprint
Abstract: We consider relatively prime integer numbers $m$ and $n$ such that each group of order $mn$ has a normal subgroup of order $m$. We prove that any skew brace of size $mn$ has an ideal of size $m$ and, if the subgroup of order $m$ of its additive group is abelian, a subbrace of size $n$. We give a method to classify skew braces of size $mn$, such that the subgroup of order $m$ of their additive group is abelian, from the classification of braces of size $m$ and the classification of skew braces of size $n$. We apply this result to determine all skew braces of size $p^2q^2$ of non-abelian type, for $p$ and $q$ odd primes, $p
Source: arXiv (Cornell University)
Author: Crespo, Teresa
Institution: Universitat de Barcelona
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214030821