Articles written in Proceedings – Mathematical Sciences

    • Palindromic widths of nilpotent and wreath products

      Valeriy G Bardakov Oleg V Bryukhanov Krishnendu Gongopadhyay

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      We prove that the nilpotent product of a set of groups $A_1, \ldots , A_s$ has finite palindromic width if and only if the palindromic widths of $A_i$, $i = 1, \ldots , s$, are finite. We give a new proof that the commutator width of $F_n \wr K$ is infinite, where $F_n$ is a free group of rank $n\geq 2$ and $K$ is a finite group. This result, combining with a result of Fink [9] gives examples of groups with infinite commutator width but finite palindromic width with respect to some generating set.

    • Rota--Baxter operators on groups


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      The theory of Rota--Baxter operators on rings and algebras has been developed since 1960. In 2020, the notion of Rota--Baxter operator on a group was defined. Further, it was proved that one may define a skew left brace on any group endowed with a Rota--Baxter operator. Thus, a group endowed with a Rota--Baxter operator gives rise to a set-theoretical solution to the Yang--Baxter equation. We provide some general constructions of Rota--Baxter operators on a group. Given a map on a group, we study its extensions to a Rota--Baxter operator. We state the connection between Rota--Baxter operators on a group and Rota--Baxter operators on an associated Lie ring. We describe Rota--Baxter operators on sporadic simple groups.

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