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

We describe groups elementarily equivalent to a free metabelian group with n generators. We also explore an exponentiation that naturally occurs in metabelian groups.

The group $PGL(2,q)$ acts $3$-transitively on the projective line $GF(q) \cup \{\infty\}$. Thus, an orbit of its action on the $k$-subsets of the projective line is the block set of a $3$-$(q+1,k,\lambda)$ design. We find the parameters of…

This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all…

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

We give some bounds on edge Folkman numbers.

We make a list of finite simple groups whose group rings over a given field are serial.

A group in which every element commutes with its endomorphic images is called an $E$-group. Our main result is that all 3-generator $E$-groups are abelian. It follows that the minimal number of generators of a finitely generated non-abelian…

We construct a Borel maximal cofinitary group.

This work obtains all the right ideals, radicals, congruences and ideals of the affine near-semirings over Brandt semigroups.

We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…

We characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of…

A search for exotic unstable neutral and charged heavy leptons as well as for stable charged heavy leptons is performed with the L3 detector at LEP. Sequential, vector and mirror natures of heavy leptons are considered. No evidence for…

An approach to a classification of groups generated by 3-state automata over a 2-letter alphabet and the current progress in this direction are presented. Several results related to the whole class are formulated. In particular, all finite,…

ECM survey article discussing the structure of subsets of Abelian groups which behave `a bit like' cosets (of subgroups).

In this article, we give some characterization results offuzzy left(right) ideals, fuzzy generalized bi-ideals and -fuzzy bi-ideals of an LA-semigroup. We also give some characterizations of LA-semigroups by the properties of fuzzy ideals.

We give a uniform description of the decomposition of the unipotent variety of a classical group in arbitrary characteristic into pieces (considered in a non-uniform way in the earlier parts of this paper).

In this expository article, we survey the rapidly emerging area of random geometric simplicial complexes.

In this paper we characterize when a Cayley automaton semigroup is a group, is trivial, is finite, is free, is a left zero semigroup, or is a right zero semigroup.

In this paper, we study the proportion of vanishing elements of finite groups. We show that the proportion of vanishing elements of every finite non-abelian group is bounded below by $1/2$ and classify all finite groups whose proportions of…

We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy…