Related papers: A characterization of Ext(G,Z) assuming V=L

We prove that if $p$ is a selective ultrafilter then ${\mathbb Q}^{(\kappa)}$ has a $p$-compact group topology without non-trivial convergent sequences, for each infinite cardinal $\kappa =\kappa^\omega$. In particular, this gives the first…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

We prove that every subnormal subgroup of p-power index in a right-angled Artin group is conjugacy p-separable. As an application, we prove that every right-angled Artin group is conjugacy separable in the class of torsion-free nilpotent…

Let G be a torsion--free abelian group of finite rank. The automorphism group Aut(G) acts on the set of maximal independent subsets of G. The orbits of this action are the isomorphism classes of indecomposable decompositions of G. G…

(withdrawn.) For every lambda we give an explicit construction of an Abelian group with no non-trivial automorphisms. In particular the group absolutely has no non-trivial automorphisms, hence is absolutely indecomposable. Earlier we knew a…

In this note, we prove: \medskip \noindent {\bf Theorem A:} \emph{ There is a fixed constant $C$ such that for any positive integer $n$ and prime $p$, every finite subgroup $G$ of order coprime to $p$ of ${\rm GL}(n,\mathbb{C})$ has an…

We will answer a question raised by Emmanuel Dror Farjoun concerning the existence of torsion-free abelian groups G such that for any ordered pair of pure elements there is a unique automorphism mapping the first element onto the second…

We obtain a forcing construction that shows that it is consistent that the torsion-free Abelian group $\mathbb{Q}^{(\lambda)}$ admits a Hausdorff group topology which is also $\mathcal{U}$-compact and contains no non-trivial convergent…

Let $p$ be a prime number. A longstanding conjecture asserts that every finite non-abelian $p$-group has a non-inner automorphism of order $p$. In this paper, we prove that if $G$ is an odd order finite non-abelian monolithic $p$-group such…

Assume $G$ is a solvable group whose elementary abelian sections are all finite. Suppose, further, that $p$ is a prime such that $G$ fails to contain any subgroups isomorphic to $C_{p^\infty}$. We show that if $G$ is nilpotent, then the…

Let $m,n$ be positive integers and $p$ a prime. We denote by $\nu(G)$ an extension of the non-abelian tensor square $G \otimes G$ by $G \times G$. We prove that if $G$ is a residually finite group satisfying some non-trivial identity $f…

We call a group FJ if it satisfies the $K$- and $L$-theoretic Farrell-Jones conjecture with coefficients in $\mathbb Z$. We show that if $G$ is FJ, then the simple Borel conjecture (in dimensions $\ge 5$) holds for every group of the form…

Let B be the complex n-dimensional ball and X' be the toroidal compactification of a quotient B/G by a torsion free lattice G of SU(n,1). For an arbitrary G-rational boundary point p, denote by U(p) the commutant of the unipotent radical of…

It has been claimed by Halmos in [Comment on the real line, Bull. Amer. Math. Soc., 50 (1944), 877-878] that if G is a Hausdorff locally compact topological abelian group and if the character group of G is torsion free then G is divisible.…

For all $k \ge 2$, we show that there exists a group $G$ and a non-free stably free $\mathbb{Z} G$-module of rank $k$. We use this to show that, for all $k \ge 2$, there exist homotopically distinct finite $2$-complexes with fundamental…

Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of arbitrary automorphic forms on $G(\mathbb…

We strengthen a result of Bagaria and Magidor~\cite{MR3152715} about the relationship between large cardinals and torsion classes of abelian groups, and prove that (1) the \emph{Maximum Deconstructibility} principle introduced in…

In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional properties of interest. We deduce from this that countable…

Let $G$ be a hyperbolic group that splits as a graph of free groups with cyclic edge groups, and which is not isomorphic to a free product of free and surface groups. We show that $G$ admits an exhausting, nested sequence of finite-index…

Let $p$ be a prime and let $G$ be a subgroup of a Sylow pro-$p$ subgroup of the group of automorphisms of the $p$-adic tree. We prove that if $G$ is fractal and $|G':\mathrm{st}_G(1)'|=\infty$, then the set $L(G)$ of left Engel elements of…