Related papers: More Abelian groups with free duals

We present sufficient conditions for the triviality of the automorphism group of regular Toeplitz subshifts and give a broad class of examples from the class of $\mathcal{B}$-free subshifts satisfying them, extending [10]. On the other hand…

We show that all finitely generated free-by-cyclic groups are conjugacy separable: if a finitely generated group $G$ surjects onto $\mathbb{Z}$ with free kernel, then for every pair of non-conjugate elements $g,h\in G$, there exists a…

In this paper we show that membership in finitely generated submonoids is undecidable for the free metabelian group of rank 2 and for the wreath product $\mathbb Z\wr (\mathbb Z\times \mathbb Z)$. We also show that subsemimodule membership…

A complete description of subgroups in the general linear group over a semilocal ring containing the group of diagonal matrices was obtained by Z.I.Borewicz and N.A.Vavilov. It is shown in the present paper that a similar description holds…

We prove that, given a finitely generated subgroup $H$ of a free group $F$, the following questions are decidable: is $H$ closed (dense) in $F$ for the pro-(met)abelian topology? is the closure of $H$ in $F$ for the pro-(met)abelian…

For any natural n, we construct an aleph_n-free abelian groups which have few homomorphisms to Z . For this we use ``aleph_n-free (n+1)-dimensional black boxes''. The method is relevant to e.g. construction of aleph_n-free abelian groups…

Let G be a group of automorphisms of a compact K\"ahler manifold X of dimension n and N(G) the subset of null-entropy elements. Suppose G admits no non-abelian free subgroup. Improving the known Tits alternative, we obtain that, up to…

Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. In this paper we shall characterise the largest possible sum-free subsets of G…

We define a class $\mathcal{U}$ of solvable groups of finite abelian section rank which includes all such groups that are virtually torsion-free as well as those that are finitely generated. Assume that $G$ is a group in $\mathcal{U}$ and…

We give an alternative proof to Agol's classification of parabolic generating pairs of non-free Kleinian groups generated by two parabolic transformations. As an application, we give a complete characterisation of epimorphims between…

There are Noetherian rings (in fact domains) with a free additive group, in every infinite cardinality. (This is an expanded version of [SgSh:217] which appears in the Abstracts of the American Mathematical Society 7 (1986): 369.)

Let $G$ be a finite abelian group and $p$ be the smallest prime dividing $|G|$. Let $S$ be a sequence over $G$. We say that $S$ is regular if for every proper subgroup $H \subsetneq G$, $S$ contains at most $|H|-1$ terms from $H$. Let…

Let $F_m$ be the free group on $m$ generators and let $G$ be a finite nilpotent group of non square-free order; we show that for each $m\ge 2$ the integral group ring ${\bf Z}[G\times F_m]$ has infinitely many stably free modules of rank 1.

We address two questions of Simon Thomas. First, we show that for any n>2 one can find a four generated free subgroup of SLn(Z) which is profinitely dense. More generally, we show that an arithmetic group \Gamma which admits the congruence…

We define abelian extensions of algebras in congruence-modular varieties. The theory is sufficiently general that it includes, in a natural way, extensions of R-modules for a ring R. We also define a cohomology theory, which we call clone…

By strengthening known results about primitivity-blocking words in free groups, we prove that for any nontrivial element w of a free group of finite rank, there are words that cannot be subwords of any cyclically reduced automorphic image…

An abelian group acting freely on a $\mathrm{CAT}(0)$ cube complex is free abelian.

Using finite abelian automorphism groups of $K3$ we construct orbifold candidates for Type IIA-heterotic dual pairs with maximal supersymmetry in six and lower dimensions. On the heterotic side, these results extend the series of known…

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…

Given an action of a group G on a topological space X, we establish a necessary and sufficient condition for the existence of a free subgroup F of rank 2 of G acting properly discontinuously on at least one nonempty, open, F-invariant…