Abstract The notion of Rota-Baxter groups was recently introduced by Guo, Lang and Sheng
[19] in the geometric study of Rota-Baxter Lie algebras. They are closely related to skew …

The second cohomology group of a left skew brace with coefficients in a trivial left brace with
non-trivial actions is defined, its connection with extensions of a left skew brace by a trivial …

In this paper, we describe the split exact sequences of skew left braces. We define a free
action of the second cohomology group of a skew left brace H by Ann (I) on Ext α (H, I) and …

Relative Rota--Baxter groups, a generalization of Rota--Baxter groups, are closely
connected to skew left braces, which play a fundamental role in understanding non …

Assume $ G $ is a finite $ p $-group, and let $ S $ be a Sylow $ p $-subgroup of
$\operatorname {Aut}(G) $ with $\exp (S)= q $. We prove that if $ G $ is of class $ c $, then …

We develop the Well's derivation for extensions realizing affine datum in arbitrary varieties;
in particular, we show there is an exact sequence connecting the group of compatible …

Let $ G $ be a finite group. By a sequence over $ G $, we mean a finite unordered string of
terms from $ G $ with repetition allowed, and we say that it is a product-one sequence if its …

Abstract Relative Rota–Baxter groups are generalizations of Rota–Baxter groups and share
a close connection with skew left braces. These structures are well-known for offering …

Cycle sets are known to give non-degenerate unitary solutions of the Yang--Baxter equation
and linear cycle sets are enriched versions of these algebraic systems. The paper explores …

We study the direct product of the automorphism groups of a finite number of groups. This is
always isomorphic to a subgroup of the automorphism group of the direct product of the …