Related papers: Minimal bounded index subgroup for dependent theor…

The number of subgroups and the number of cyclic subgroups are natural combinatorial invariants of a finite group. We investigate how restrictions on these quantities, together with the number of distinct prime divisors of $|G|$, enforce…

For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.

If a finite p-group G acts continuously on a compact topological manifold M then, with some bound C depending on M alone, G has a subgroup H of index at most C such that the H-action on M has at most C stabilizer subgroups. This result…

Given a group $G$, we write $g^G$ for the conjugacy class of $G$ containing the element $g$. A theorem of B. H. Neumann states that if $G$ is a group in which all conjugacy classes are finite with bounded size, then the commutator subgroup…

Given a definably amenable approximate subgroup $A$ of a (local) group in some first-order structure, there is a type-definable subgroup $H$ normalised by $A$ and contained in $A^4$ such that every definable superset of $H$ has positive…

We consider a few types of bounded homomorphisms on a topological group. These classes of bounded homomorphisms are, in a sense, weaker than the class of continuous homomorphisms. We show that with appropriate topologies each class of these…

We settle some open problems in the special case of groups in o-minimal structures, such as the equality of G^00 and G^000 and the equivalence of definable amenability and existence of a type with bounded orbit. We prove almost exactness of…

The Tits core G^+ of a totally disconnected locally compact group G is defined as the abstract subgroup generated by the closures of the contraction groups of all its elements. We show that a dense subgroup is normalised by the Tits core if…

Let R be a complete rank-1 valuation ring of mixed characteristic (0,p), and let K be its field of fractions. A g-dimensional truncated Barsotti-Tate group G of level n over R is said to have a level-n canonical subgroup if there is a…

We give examples of groups G such that G^00 is different from G^000. We also prove that for groups G definable in an o-minimal structure, G has a "bounded orbit" iff G is definably amenable. These results answer questions of Gismatullin,…

We determine all groups definable in Presburger arithmetic, up to a finite index subgroup.

A group G is a cn-group if for each subgroup H of G there exists a normal subgroup N of G such that the index of both H and N in HN is finite. The class of cn-groups contains properly the classes of core- finite groups and that of groups in…

Let G be a linear algebraic group defined over a finite field F_q. We present several connections between the isogenies of G and the finite groups of rational points G(F_q^n). We show that an isogeny from G' to G over F_q gives rise to a…

We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: for every $\theta$ there is a dependent theory $T$ of size $\theta$ such that for all $\kappa$ and $\delta$,…

We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.

In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…

Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an…

We present a diagram surveying equivalence or strict implication for properties of different nature (algebraic, model theoretic, topological, etc.) about groups definable in o-minimal structures. All results are well-known and an extensive…

Let G be a group definable in an o-minimal structure M. We prove that the union of the Cartan subgroups of G is a dense subset of G. When M is an expansion of a real closed field we give a characterization of Cartan subgroups of G via their…

We propose a semantically grounded theory of session types which relies on intersection and union types. We argue that intersection and union types are natural candidates for modeling branching points in session types and we show that the…