Related papers: A Borel maximal cofinitary group
We construct the first examples of residually finite non-exact groups. The construction is based on author's earlier construction of groups containing isometrically expanders using a graphical small cancellation.
We give a structural theorem for pseudofinite groups of finite centraliser dimension. As a corollary, we observe that there is no finitely generated pseudofinite group of finite centraliser dimension.
We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type.
We construct examples of non-bi-orderable one-relator groups without generalized torsion. This answers a question asked in [2].
In this paper, we study a group in which every 2-maximal subgroup is a Hall subgroup.
We prove that there are only finitely many conjugacy classes of arithmetic maximal hyperbolic reflection groups.
We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)-space.
We describe finite soluble groups in which every $n$-maximal subgroup is $\mathfrak F$-subnormal.
A proof of the Borel completeness of torsion free abelian groups is presented. This proof differs considerably from the approach of Paolini-Shelah.
We develop a new forcing notion for adjoining self-coding cofinitary permutations and use it to show that consistently, the minimal cardinality $\mathfrak a_{\text{g}}$ of a maximal cofinitary group (MCG) is strictly between $\aleph_1$ and…
We classify finite groups $G$ in $\mathrm{PGL}_{4}(\mathbb{C})$ such that $\mathbb{P}^3$ is $G$-birationally rigid.
We construct a Borel graph G such that ZF+DC+"There are no maximal independent sets in G" is equiconsistent with ZFC+"There exists an inaccessible cardinal".
We construct new classes of self-similar groups : S-aritmetic groups, affine groups and metabelian groups. Most of the soluble ones are finitely presented and of type FP_{n} for appropriate n.
We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.
We give a description of a finite group whose maximal subgroups possess only soluble proper subgroups, which implies the answer to the well-known question on composition factors of finite groups, whose second maximal subgroups are soluble.
Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…
We develop the theory of $H$-graded manifolds for any finitely generated abelian group, using tools from representation theory. Furthermore, we introduce and investigate the notion of $H$-graded coverings of supermanifolds in the case where…
We present an elliptic version of Selberg's integral formula.
We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.
We give an elementary proof that there are two topological generators for the full group of every aperiodic hyperfinite probability measure preserving Borel equivalence relation. Our proof explicitly constructs topological generators for…