Related papers: Nilpotent left quasigroups
We formulate and prove relative versions of several classical decompositions known in the theory of Chevalley groups over commutative rings. As an application we obtain upper estimates for the width of principal congruence subgroups in…
A quandle is a self-distributive algebraic structure that appears in quasi-group and knot theories. For each abelian group A and c \in A we define a quandle G(A, c) on \Z_3 \times A. These quandles are generalizations of a class of…
We describe the structure of "K-approximate subgroups'' of solvable subgroups of GL_n(C), showing that they have a large nilpotent piece. By combining this with the main result of our recent paper on approximate subgroups of torsion-free…
In this paper, we establish the theory of nilpotent hypergroups and study some properties of nilpotent hypergroups and provided some structural characterizations of nilpotent hypergroups.
We define a class of quandle-like structures called pseudoquandles and analyze some of their algebraic properties.
The fundamental quandle is a powerful invariant of knots and links, but it is difficult to describe in detail. It is often useful to look at quotients of the quandle, especially finite quotients. One natural quotient introduced by Joyce is…
The binary products of right, left or double division in semigroups that are semilattices of groups give interesting groupoid structures that are in one to one correspondence with semigroups that are semilattices of groups. This work is…
The article deals with profinite groups in which the centralizers are pronilpotent (CN-groups). It is shown that such groups are virtually pronilpotent. More precisely, let G be a profinite CN-group, and let F be the maximal normal…
This article lays the foundations for an analogue of geometric group theory that studies actions on graphs by right quasigroups, including racks and quandles. We study markings of graphs that realize racks, and we introduce (di)graph…
We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the length tend to infinity. Whereas random groups are quotients…
We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.
We study the connection between amenability, F{\o}lner conditions and the geometry of finitely generated semigroups. Using results of Klawe, we show that within an extremely broad class of semigroups (encompassing all groups, left…
In the present paper, as a continuation of our preceding paper [10], we study another kind of central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a viewpoint of discrete geometric analysis…
In this article we provide evidence for a well-known conjecture which states that quasi-isometric simply-connected nilpotent Lie groups are isomorphic. We do so by constructing new examples which are rigid in the sense that whenever they…
A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be expressed as a# b where a and b are elements of S and if, in addition, every element of S that is square…
We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to define left and right nilpotent skew left braces. Several results related to these concepts are proved and…
In studying nilpotent groups, the lower central series and other variations can be used to construct an associated $\mathbb{Z}^+$-graded Lie ring, which is a powerful method to inspect a group. Indeed, the process can be generalized…
In the present paper, we study central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a point of view of discrete geometric analysis developed by Kotani and Sunada. We establish a semigroup CLT for a…
This article addresses two central problems in the theory of quandle rings. First, motivated by Conjecture 3.10 in Internat. J. Math. 34 (2023), no. 3, Paper No. 2350011: for a semi-latin quandle $X$, every nonzero idempotent in the…
Quandles are self-distributive, right-invertible, idempotent algebras. A group with conjugation for binary operation is an example of a quandle. Given a quandle $(Q, \ast)$ and a positive integer $n$, define $a\ast_n b = (\cdots (a\ast…