In [Rum18], Rump defined and characterized noncommutative universal groups G(X) for generalized orthomodular lattices X.We give an explicit description of G(X) in terms of paraunitary matrix groups, whenever X is the orthomodular lattice of subspaces of a finite-dimensional k-vector space V that is equipped with an anisotropic, symmetric k-bilinear form.Date: September 25, 2018.
In this paper, we classify the left braces of order [Formula: see text], where [Formula: see text] are primes fulfilling [Formula: see text]. This classification includes a proof of three conjectures of Guarnieri and Vendramin concerning the number of isomorphism classes of left braces of order [Formula: see text] for certain values of [Formula: see text].
Let p and q be different prime numbers. Using recent results of Cedó and Okniński, we describe isomorphism classes of indecomposable set-theoretic solutions to the Yang-Baxter equation of cardinality pq.
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