Related papers: Nice enumerations of omega-categorical groups

We prove that every many-sorted $\omega$-categorical theory is completely interpretable in a one-sorted $\omega$-categorical theory. As an application, we give a short proof of the existence of non $G$--compact $\omega$-categorical…

A group is called capable if it is a central factor group. We consider the capability of certain nilpotent products of cyclic groups, and obtain a generalisation of a theorem of Baer for the small class case. The approach may also be used…

Let $\mathcal{V}$ be a congruence permutable variety generated by a finite nilpotent algebra $\mathbf{A}$. If $\mathbf{A}$ is a product of algebras of prime power order, then the class $\mathcal{V}_\text{si}$ of subdirectly irreducible…

We consider the class of finitely generated groups which have a normal form computable in logspace. We prove that the class of such groups is closed under finite extensions, finite index subgroups, direct products, wreath products, and also…

The class of all subdirectly irreducible groups belonging to a variety generated by a finite nilpotent group can be axiomatised by a finite set of elementary sentences.

A topological group $G$ is said to have a local $\omega^\omega$-base if the neighbourhood system at identity admits a monotone cofinal map from the directed set $\omega^\omega$. In particular, every metrizable group is such, but the class…

This work presents an example of a finitely presented semigroup $S$ containing an infinite nonnilpotent nil ideal $LS$, whose elements do not have a square (i.e. any word of the type $LXYYZ$ equals zero.)

We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

We evaluate in closed form three special classes of alternating zeta series with one and two additional parameters. Two classes are expressed as linear combinations of polylogarithms while for the third class we prove an expression…

We compute the representation and class counting zeta functions for a family of torsion-free finitely generated nilpotent groups of nilpotency class $2$. These groups arise from a generalisation of one the families of unipotent groups…

Let $G$ be a finite group and $K$ a splitting field of $G$ of characteristic $p>0$. Denote by $KG$ the group algebra of $G$ over $K$ and $Z(KG)$ the center of $KG$. Let $V_G$ be the $K$-subspace of trace-zero elements of $KG$. We give some…

Taking into account the theoretical results and guidelines given inthis work, we introduce a computational method to construct any 2 step nilpotent quadratic algebra of d generators. Along the work we show that the key of the classification…

We use topological methods to study the maximal subgroups of the free idempotent generated semigroup on a biordered set. We use these to give an example of a free idempotent generated semigroup with maximal subgroup isomorphic to the free…

We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex numbers. We write explicit structure constants for these real Lie algebras.

The aim of this note is to prove that there are $2^{\aleph_0}$ non-isomoprhic 2-generated just-infinite branch pro-$2$ groups.

We show that a linear group without unipotent elements of infinite order possesses properties akin to those held by groups of non positive curvature. Moreover in positive characteristic any finitely generated linear group acts properly and…

We describe $\{2,3\}$-groups in which the order of a product of any two elements of orders at most $4$ does not exceed $9$ and the centralizer of every involution is a locally cyclic $2$-subgroup. In particular, we will prove that these…

We construct uncountably many discrete groups of type $FP$; in particular we construct groups of type $FP$ that do not embed in any finitely presented group. We compute the ordinary, $\ell^2$- and compactly-supported cohomology of these…

Motivated by examples in infinite group theory, we classify the finite groups whose subgroups can never be decomposed as direct products.

We provide new examples of groups without rational cross-sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Specifically, our examples are extensions of infinite torsion…