Related papers: Chief factors in Polish groups
In 'The essentially chief series of a compactly generated locally compact group', an analogue of chief series for finite groups is discovered for compactly generated locally compact groups. In the present article, we show that chief factors…
In group theory the chief factors allow a group to be studied by its representation theory on particularly natural irreducible modules. It is to be expected, therefore, that they will play an important role in the study of Lie algebras. In…
We give strong necessary conditions on the admissibility of a Polish group topology for an arbitrary graph product of groups $G(\Gamma, G_a)$, and use them to give a characterization modulo a finite set of nodes. As a corollary, we give a…
The set of increasing functions on the rational numbers, equipped with the composition operation, naturally forms a topological semigroup with respect to the topology of pointwise convergence in which a sequence of increasing functions…
We give a complete characterization of the graph products of cyclic groups admitting a Polish group topology, and show that they are all realizable as the group of automorphisms of a countable structure. In particular, we characterize the…
Sorin Popa initiated the study of Polish groups which are embeddable into the unitary group of a separable finite von Neumann algebra. Such groups are called of finite type. We give necessary and sufficient conditions for Polish groups to…
We first obtain finiteness properties for the collection of closed normal subgroups of a compactly generated locally compact group. Via these properties, every compactly generated locally compact group admits an essentially chief series -…
We introduce and study Polish topologies on various spaces of countable enumerated groups, where an enumerated group is simply a group whose underlying set is the set of natural numbers. Using elementary tools and well known examples from…
A general overview of the phenomenon of automatic continuity of homomorphisms between Polish groups is given. In particular, we study variants and improvements of the closed graph theorem, applying these to the problem of continuity of…
In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid $\operatorname{End}(\mathbb{A})$ of a countable relational structure $\mathbb{A}$. As applications, we show…
We study the question how quickly products of a fixed conjugacy class in the projective unitary group of a II${}_1$-factor von Neumann algebra cover the entire group. Our result is that the number of factors that are needed is essentially…
We survey three methods for proving that the characteristic polynomial of a finite lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on…
We prove that every Polish group with more than two elements admits a non-trivial topological group automorphism. As a consequence, a hypothetical uniquely homogeneous Polish space with more than two points cannot be a semitopological…
We apply the theory of large-scale geometry of Polish groups to groups of absolutely continuous homeomorphisms. Let $M$ be either the compact interval or circle. We prove that the Polish group $\operatorname{AC}_+(M)$ of…
We present algorithms for the group independent reduction of group theory factors of Feynman diagrams. We also give formulas and values for a large number of group invariants in which the group theory factors are expressed. This includes…
We show that any separated essentially finite-type map $f$ of noetherian schemes globally factors as $f = hi$ where $i$ is an injective localization map and $h$ a separated finite-type map. In particular, via Nagata's compactification…
The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between…
This expository paper is intended for a short self-contained introduction to the theory of infinite convolutions of probability measures on Polish semigroups. We give the proofs of the Rees decomposition theorem of completely simple…
We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…
One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group $G/\zeta(G)$ of a group $G$ is finite, then its derived subgroup $[G,G]$ is also finite. This result has numerous…