Related papers: Left $3$-Engel elements in groups: A survey
Engel groups and Engel elements became popular in 50s. We consider in the paper the more general nil-groups and nil-elements in groups. All these notions are related to nilpotent groups and nilpotent radicals in groups. These notions…
In this paper we study numerical semigroups generated by three elements. We give a characterization of pseudo-symmetric numerical semigroups. Also, we will give a simple algorithm to get all the pseudo-symmetric numerical semigroups with…
Various uses of the renormalization group are examined.
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.
This survey paper aims at giving the state of the art in the study of string C-group representations of almost simple groups. It also suggest a series of problems and conjectures to the interested reader.
Let $\Gamma$ be the first Grigorchuk group. According to a result of Bartholdi, the only left Engel elements of $\Gamma$ are the involutions. This implies that the set of left Engel elements of $\Gamma$ is not a subgroup. Of particular…
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
We classify irreducible actions of connected groups of finite Morley rank on abelian groups of Morley rank 3.
In this survey we review recent results on left-invariant conformal Killing p-forms on Lie groups endowed with a left-invariant metric. We also mention interesting open questions that could lead into future research.
We review recent progress in the studies of left handed materials.
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
We introduce the notions of one-sided dirings, 3-irreducible left modules, 3-primitive left dirings, 3-semi-primitive left dirings, 3-primitive ideals and 3-radicals. The main results consists of two parts. The first part establishes two…
We review the progress made at LEP in the quest for new particles.
We propose a list of open problems in numerical semigroups.
A random group contains many quasiconvex surface subgroups.
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…
A survey of results on the residual properties of Baumslag -- Solitar groups which have been obtained to date.
We count number of groupoids of order 3 with some Bol-Moufang type identities.
We present several formulas for the traces of elements in complex hyperbolic triangle groups generated by complex reflections. The space of such groups of fixed signature is of real dimension one. We parameterise this space by a real…