Erratum to: “Elementary embeddings in torsion-free hyperbolic groups”
Existency-Closed Groups in X_1 with Special Properties
Finite images and elementary equivalence of completely regular inverse semigroups.
First Order Classes of Groups Having no Groups With a Given Property
Foundations of the Theory of Groupoids and Groups [Book]
Group conjugation has non-trivial LD-identities
We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.
Group Theory and Architecture, 2: Why Symmetry/Asymmetry?
Group theory based at any point.
Groupes nilpotents existentiellement clos de classe fixée
Groups – Additive Notation
We translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25]. In particular, these authors have defined the notions of group, abelian group, power of an element of a group, order of a group and order of an element, subgroup, coset of a subgroup, index of a subgroup, conjugation, normal subgroup, topological group, dense subset and basis...
Hyperidentities of groups and semigroups.
Hyperidentities of groups and semigroups. (Short Communication).
Inert subgroups of uncountable locally finite groups
Let be an uncountable universal locally finite group. We study subgroups such that for every , .
Infinitary stationary logic and abelian groups
Interpreting number theory in nilpotent groups.
Kleinian groups (a survey)
Le groupe des métamorphoses d'une catégorie, un exemple
Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras
This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The...
Limits of relatively hyperbolic groups and Lyndon’s completions
We describe finitely generated groups universally equivalent (with constants from in the language) to a given torsion-free relatively hyperbolic group with free abelian parabolics. It turns out that, as in the free group case, the group embeds into the Lyndon’s completion of the group , or, equivalently, embeds into a group obtained from by finitely many extensions of centralizers. Conversely, every subgroup of containing is universally equivalent to . Since finitely generated...
Localizing groups with action.
When localizing the semidirect product of two groups, the effect on the factors is made explicit. As an application in Topology, we show that the loop space of a based connected CW-complex is a P-local group, up to homotopy, if and only if π1X and the free homotopy groups [Sk-1, ΩX], k ≥ 2, are P-local.