Related papers: An antichain condition for infinite groups

Odifreddi asked whether every non-irreducible many-one degree must contain an infinite antichain of one-one degrees. Positive answers are known for computably enumerable many-one degrees (Degtev) and, more recently, for many-one degrees…

We generalize Kada's definable strengthening of Dilworth's characterization of the class of quasi-orders admitting an antichain of a given finite cardinality.

We prove that every interval order $P$ with no infinite antichain has a Gallai decomposition. That is, $P$ is a lexicographical sum of proper interval orders over a chain, an antichain or a prime interval order. This is a consequence of the…

Let $(X,T)$ be a Cantor minimal system, and let $\Gamma$ denote either its associated topological full group or the full group of a Bratteli diagram associated with $(X,T)$. In this paper we describe the structure of indecomposable…

Let $G$ be a finite group, and $\alpha$ a nontrivial character of $G$. The McKay graph $\mathcal{M}(G,\alpha)$ has the irreducible characters of $G$ as vertices, with an edge from $\chi_1$ to $\chi_2$ if $\chi_2$ is a constituent of…

It is known that any locally graded group with finitely many derived subgroups of non-normal subgroups is finite-by-abelian. This result is generalized here, by proving that in a locally graded group $G$ the subgroup $\gamma_{k}(G)$ is…

Let $\varphi\colon\Gamma\to G$ be a homomorphism of groups. In this paper we introduce the notion of a subnormal map (the inclusion of a subnormal subgroup into a group being a basic prototype). We then consider factorizations…

Restriction is a natural quasi-order on $d$-way tensors. We establish a remarkable aspect of this quasi-order in the case of tensors over a fixed finite field -- namely, that it is a well-quasi-order: it admits no infinite antichains and no…

We study the fundamental group of an open $n$-manifold $M$ of nonnegative Ricci curvature with additional stability condition on $\widetilde{M}$, the Riemannian universal cover of $M$. We prove that if any tangent cone of $\widetilde{M}$ at…

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the…

It is an open question in the study of Chermak-Delgado lattices precisely which finite groups $G$ have the property that $CD(G)$ is a chain of length $0$. In this note, we determine two classes of groups with this property. We prove that if…

We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…

The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of centralizers each having…

Anti-elementarity is a strong way of ensuring that a class of structures , in a given first-order language, is not closed under elementary equivalence with respect to any infinitary language of the form L $\infty$$\lambda$. We prove that…

A semigroup $S$ is said to be right pseudo-finite if the universal right congruence can be generated by a finite set $U\subseteq S\times S$, and there is a bound on the length of derivations for an arbitrary pair $(s,t)\in S\times S$ as a…

Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…

In the setting of Carnot groups, we are concerned with the rectifiability problem for subsets that have finite sub-Riemannian perimeter. We introduce a new notion of rectifiability that is, possibly, weaker than the one introduced by…

Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the $ \Pi $-property in $ G $ if $ | G/K : N_{G/K}((H \cap L)K/K)| $ is a $ \pi(( H \cap L)K/K ) $-number for any chief factor $ L/K $ of $ G $; and we call that $…

An $\mathfrak{M}_C$ group is a group in which all chains of centralizers have finite length. In this article, we show that every nilpotent subgroup of an $\mathfrak{M}_C$ group is contained in a definable subgroup which is nilpotent of the…

Let $ G $ be a finite group and $ \chi \in \mathrm{Irr}(G) $. Define $ \mathrm{cv}(G)=\{\chi(g)\mid \chi \in \mathrm{Irr}(G), g\in G \} $, $ \mathrm{cv}(\chi)=\{\chi(g)\mid g\in G \} $ and denote $ \mathrm{dl}(G) $ by the derived length of…