Related papers: Left $3$-Engel elements in groups: A survey

Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian group of order $q^r$ with $r\geq2$ acting on a finite $q'$-group $G$. The following results are proved. We show that if all elements in $\gamma_{r-1}(C_G(a))$ are…

We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.

The fundamental groups of compact 3-manifolds are known to be residually finite. Feng Luo conjectured that a stronger statement is true, by only allowing finite groups of the form $PGL(2,R),$ where $R$ is some finite commutative ring with…

In this paper the third homology group of the linear group GL_2(R) with integral coefficients is investigated, where R is a commutative ring with many units.

We develop JSJ decomposition theory of pro-p groups.

This article provides a detailed description of some nilpotent left braces generated by one element.

This is a survey of results in the enumeration of lattice paths.

We construct a supercharacter theory for the group of invertible elements of a reduced algebra. For the case of the triangular group, we obtain the formula for values of supercharacters on superclasses.

We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices.…

We propose various problems about Borel complexity of characterized subgroups of compact abelian groups, inspired by our forthcoming paper \cite{DI3}.

We introduce the notion of a Schur-finite element in a $\lambda$-ring.

We classify complex surfaces $(M,\,J)$ admitting Engel structures $\mathcal{D}$ which are complex line bundles. Namely we prove that this happens if and only if $(M,\,J)$ has trivial Chern classes. We construct examples of such Engel…

Classification of groups generated by 3-state automata over a 2-letter alphabet started in the first paper (see http://www.arxiv.org/abs/math/0612178) is continued.

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.

Ideal series of semigroups play an important role in the examination of semigroups which have proper two-sided ideals. But the corresponding theorems cannot be used when left simple (or right simple or simple) semigroups are considered. So…

We introduce an algebraic framework for the description of baryons. Within this framework we study a collective string-like model and show that this model gives a good overall description of the presently available data. We discuss in…

Let R be an associative ring with unity and let [R] and U(R) denote the associated Lie ring (with [a,b]=ab-ba) and the group of units of R, respectively. In 1983 Gupta and Levin proved that if [R] is a nilpotent Lie ring of class c then…

We calculate certain ext-groups between modules for a linear algebraic group. The results are in agreement with the Lusztig conjecture.

We prove that a finite $3$-group in the Cremona group $\mathrm{Cr}_3(\mathbb{C})$ can be generated by at most $4$ elements. This provides the last missing piece in bounding the ranks of finite $p$-subgroups in the space Cremona group.

A class of groups is investigated, each of which has a fairly simple presentation . For example the group $R = (a, b, c, d | a^3 = b^3 = c^3 = d^3 = 1, ba^{-1} =dc^{-1}, ca^{-1} = db^{-1}) $ is in the class. Such a group does not have as a…