Related papers: Minimal clones with weakly abelian representations

We prove that a finitely generated group contains a sequence of non-trivial elements which converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian.

Let $G$ be a nonabelian group. We say that $G$ has an abelian partition, if there exists a partition of $G$ into commuting subsets $A_1, A_2, \ldots, A_n$ of $G$, such that $|A_i|\geqslant 2$ for each $i=1, 2, \ldots, n$. This paper…

We present two minimal clones containing 26 and 78 majority operations respectively, more than any other previously known example.

Given a subset $W$ of an abelian group $G$, a subset $C$ is called an additive complement for $W$ if $W+C=G$; if, moreover, no proper subset of $C$ has this property, then we say that $C$ is a minimal complement for $W$. It is natural to…

Based on an idea in [Gan--Savin, Represent. Theory (2005)], we give a classification of minimal representations of connected simple real Lie groups not of type $A$. Actually, we prove that there exist no new minimal representations up to…

We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also…

The aim of this note is to give an effective criterion to verify whether a cubic polynomial over a non-Archimedean field has a weak N\'{e}ron model or not.

We determine the minimal polynomial of each element of the double cover $G$ of the symmetric or alternating group in every irreducible spin representation of $G$.

We discuss various constructions which allow one to embed a principally polarized abelian variety in the jacobian of a curve. Each of these gives representatives of multiples of the minimal cohomology class for curves which in turn produce…

We relate endotrivial representations of a finite group in characteristic p to equivariant line bundles on the simplicial complex of non-trivial p-subgroups, by means of weak homomorphisms.

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

If A and B are abelian varieties over a number field K such that there are non-trivial geometric homomorphisms of abelian varieties between reductions of A and B at most primes of K, then there exists a non-trivial (geometric) homomorphism…

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable…

We say that an infinite word w is weak abelian periodic if it can be factorized into finite words with the same frequencies of letters. In the paper we study properties of weak abelian periodicity, its relations with balance and frequency.…

We present a series of examples of precompact, noncompact, reflexive topological Abelian groups. Some of them are pseudocompact or even countably compact, but we show that there exist precompact non-pseudocompact reflexive groups as well.…

For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of the other using operations from C. In…

We define a notion of a weak canonical base for a partial type. This notion is weaker than the usual canonical base for an amalgamation base. We prove that certain family of partial types have a weak canonical base. This family clearly…

The aim of this work is to study the representation dimension of cluster tilted algebras. We prove that the weak representation dimension of tame cluster tilted algebras is equal to three. We construct a generator module that reaches the…

We characterize having Borel isomorphism relation among some weakly minimal trivial theories, namely the examples of families of finite equivalence relations from recent joint work with Laskowski, and tame expansions of…

Let $N$ be a submodule of a finitely generated module $M$ over a Noetherian ring. A method for the computation of the submodule generated by the envelope of $N$ is given. The relations between weakly prime submodules and their envelopes are…