相关论文: On some groupoids of small orders with Bol-Moufang…

We present results about groupoids of small order with Bol-Moufang type identities both classical and non-classical which are listed in [7, 8].

A loop identity is of Bol-Moufang type if two of its three variables occur once on each side, the third variable occurs twice on each side, and the order in which the variables appear on both sides is the same, viz. $((xy)x)z=x(y(xz))$.…

A quasigroup identity is of Bol-Moufang type if two of its three variables occur once on each side, the third variable occurs twice on each side, the order in which the variables appear on both sides is the same, and the only binary…

We describe all constructions for loops of Bol-Moufang type analogous to the Chein construction $M(G,*,g_0)$ for Moufang loops.

We prolong Kunen research about existence of units (left, right, two-sided) in quasigroups with classical Bol-Moufang type identities. These identities were listed in Fenvesh article.

Some varieties of groupoids and quasigroups generated by linear-bivariate polynomials $P(x,y)=a+bx+cy$ over the ring $\mathbb{Z}_n$ are studied. Necessary and sufficient conditions for such groupoids and quasigroups to obey identities which…

We initiate (co)homology theory for quasigroups of Bol-Moufang type based on analysis of their extensions by affine quasigroups of the same type. We use these extensions to define second and third boundary operations, $\partial_2(x,y)$ and…

Automorphism groups of $2$-groups of coclass at most $3$ are investigated.

We give a brief survey of abelian torsions of 3-manifolds.

We classify the homeomorphism types of the Morse boundaries of all 3-manifold groups into 9 different possible homeomorphism types, and show how the Morse boundary depends on the geometric decomposition.

We use groups with triality to construct a series of nonassociative Moufang loops. Certain members of this series contain an abelian normal subloop with the corresponding quotient being a cyclic group. In particular, we give a new series of…

We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.

The article presents a complete classification of $n$-valued monoids and groups of order 3. Important corollaries of this result are discussed.

In this article we have constructed some examples of some classes of AG-groupoids

In this note, we present several identities involving binomial coefficients and the two kind of Stirling numbers.

Lower bounds for the number of local nearrings on groups of order $p^3$ are obtained. On each non-metacyclic non-abelian or metacyclic abelian groups of order $p^3$ there exist at least $p+1$ non-isomorphic local nearrings

We classify minimal projective 3-folds of general type with $p_g = 2$ by studying the birationality of their 6-canonical maps.

We compute the integral cohomology rings of a family of 3-groups. As a corollary, we exhibit, for each n greater than or equal to 5, a pair of groups of order 3^n whose integral cohomology rings are isomorphic.

Let $G$ be a group and $g$ a non-trivial element in $G$. If some non-empty finite product of conjugates of $g$ equals to the identity, then $g$ is called a generalized torsion element. The minimum number of conjugates in such a product is…

We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.