Related papers: Supernilpotent groups and $3$-supernilpotent loops
We give a comprehensive study of the so-called \textit{semi-tripotent rings} obtaining their new and non-trivial characterization as well as a complete description in terms of sums and products of some special elements. Particularly, we…
In this paper we study Almost-Riemannian Structures (ARS) on the class of nonnilpotent, solvable, conneted 3D Lie groups. The nice structures present in such groups allow us to show that the singular locus of ARSs on such groups are always…
Non-associative finite invertible loops (NAFIL) are loops whose every element has a unique two-sided inverse. Not much is known about the class of NAFIL loops which includes the familiar IP (Inverse Property), Moufang, and Bol loops. Our…
The unipotent groups are an important class of algebraic groups. We show that techniques used to compute with finitely generated nilpotent groups carry over to unipotent groups. We concentrate particularly on the maximal unipotent subgroup…
The paper deals with quasigroups having a trivial group of automorphisms and a trivial group of autotopisms. Examples of such quasigroups and methods of their verification are given.
If $G$ and $H$ are finitely generated residually nilpotent groups, then $G$ and $H$ are in the same nilpotent genus if they have the same lower central quotients (up to isomorphism). A stronger condition is that $H$ is para-$G$ if there…
Given a lattice $\mathbb{L}$ and a class $K$ of algebraic structures, we say that $\mathbb{L}$ \emph{forces nilpotency} in $K$ if every algebra $\mathbf{A} \in K$ whose congruence lattice $\mathrm{Con} (\mathbf{A})$ is isomorphic to…
We consider N=1 supersymmetric gauge theories based on the group SU(N)_1 x SU(N)_2 x ... x SU(N)_k with matter content (N,N*,1,...,1) + (1,N,N*,..., 1) + >... + (N*,1,1,...,N) as candidates for the unification symmetry of all particles. In…
We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a non-trivial partition, and symmetric and alternating groups.
We discuss the recent developments of semi-classical and micro-local analysis in the context of nilpotent Lie groups and for sub-elliptic operators. In particular, we give an overview of pseudo-differential calculi recently defined on…
We study the structure of nilpotent subsemigroups in the semigroup $M(n,\mathbb{F})$ of all $n\times n$ matrices over a field, $\mathbb{F}$, with respect to the operation of the usual matrix multiplication. We describe the maximal…
Our aim in this paper is to initiate the study of exponent semigroups for rational matrices. We prove that every numerical semigroup is the exponent semigroup of some rational matrix. We also obtain lower bounds on the size of such matrices…
We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence…
In this work, we show that for a certain class of threefolds in positive characteristics, rational-chain-connectivity is equivalent to supersingularity. The same result is known for K3 surfaces with elliptic fibrations. And there are…
Moufang loops are one of the best-known generalizations of groups. There is only one countable family of nonassociative finite simple Moufang loops, arising from the split octonion algebras. We prove that every member of this family is…
Machine learning is applied to find proofs, with smaller or smallest numbers of nodes, for the classification of 4-nilpotent semigroups.
Let $E/\mathbb{Q}$ be an elliptic curve. We say that $E$ has a near coincidence of level $(n,m)$ if $m \mid n$ and $\mathbb{Q}(E[n]) = \mathbb{Q}(E[m],\zeta_{n})$. We classify near coincidences of prime power level and use this result to…
Groups with commuting inner mappings are of nilpotency class at most two, but there exist loops with commuting inner mappings and of nilpotency class higher than two, called loops of Cs\"org\H{o} type. In order to obtain small loops of…
This paper is about nilpotent orbits of reductive groups over local non-Archimedean fields. In this paper we will try to identify for which groups there are only finitely many nilpotent orbits, for which groups the nilpotent orbits are…
The association of the variational method with supersymmetric quantum mechanics through an ansatz for the superpotential is reviewed and the approximate energy spectra of non-exactly solvable potentials, such like the Hulthen, the Morse and…