Braces of order $p^2q$

Carsten Dietzel

Braces of order $p^2q$

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arxiv 1801.06911 v2 pith:TEC4BIO2 submitted 2018-01-21 math.QA

Carsten Dietzel This is my paper · ORCID

classification math.QA

keywords bracesorderconjecturesleftvendraminarticlecertaincite

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abstract

In this article we classify the left braces of order $p^2q$ where $p,q$ are primes fulfilling $q > p+1$. This classification includes a proof of three conjectures of Guarnieri and Vendramin (\cite[Conjectures 6.2-6.4]{Vendramin_skew}) concerning the number of isomorphism classes of left braces of order $p^2q$ for certain values of $p,q$.

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Skew braces of size $pq$
math.GR 2019-08 accept novelty 6.0 of 10

For primes p>q, all skew braces of order pq are explicitly constructed: only the trivial brace if p is not 1 modulo q, and exactly 2q+2 braces if p is 1 modulo q.

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