… method to construct infinitely many groups of I-type (and hence infinitely many involutive non-…
A finite group with this property we will call an involutive Yang-Baxter (IYB, for short) group. …

… First, we improve a result of [3] on such solutions (X,r) for which the associated involutive
Yang–Baxter group is abelian and the set X is finite (see Theorem 3). Next, we answer two …

… of finite involutive simple solutions in which B(2), that in this case coincides with the so-called
displacement group, … 3.1], where involutive solutions with primitive permutation group were …

… A group is said to be an involutive Yang-Baxter group, or simply an IYB-group, if it is isomorphic
to the permutation group of an … finite) YB-groups as a consequence of our main theorem. …

… involutive solutions with diffuse structure groups; that only free abelian structure groups are
bi-orderable; and that for the structure group … to determine what finite groups can be obtained …

… of finite uniconnected involutive non-degenerate set-theoretic solutions of the Yang–Baxter …
In the core of the paper, we also use left braces to classify all the uniconnected involutive …

… We show that in the latter case, D2n acts as a Frobenius group on X. To exclude … group of
a finite non-degenerate involutive solution pX, rq of Eq. (1) never acts as a Frobenius group on …

… Nevertheless, we will find an ordered structure on the group G ( X ) which becomes
predominant in the degenerate case. If X is indecomposable, which means that G ( X ) acts …

… matrices a finite indecomposable involutive solution with abelian permutation group and we
… also infinite indecomposable involutive solution with abelian permutation group and finite …

… involutive partial solutions as a generalization of nondegenerate involutive set-theoretical
solutions of the quantum Yang… sense of the braid groups, and the finite-type Artin groups [28]. …