Related papers: Groups with finitely many conjugacy classes and th…

We show that if the automorphism group of a projective variety is torsion, then it is finite. Motivated by Lang's conjecture on rational points of hyperbolic varieties, we use this to prove that a projective variety with only finitely many…

We give a uniform construction that, on input of a recursive presentation $P$ of a group, outputs a recursive presentation of a torsion-free group, isomorphic to $P$ whenever $P$ is itself torsion-free. We use this to re-obtain a known…

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…

Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1. We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on…

We classify all finite groups G such that the product of any two non-inverse conjugacy classes of G is always a conjugacy class of G. We also classify all finite groups G for which the product of any two G-conjugacy classes which are not…

Using graph of groups decompositions of finitely generated groups, we define Euler characteristic type invariants which are non-zero in many interesting classes of finitely presented, hyperbolic, limit and CSA groups, including elementarily…

Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…

We prove that every finitely generated group $G$ discriminated by a locally quasi-convex torsion-free hyperbolic group $\Gamma$ is effectively coherent: that is, presentations for finitely generated subgroups can be computed from the…

Let S be a generating set of a group G. We say that G has FINITE WIDTH relative to S if G=(S\cup S^{-1})^k for a suitable natural number k. We say that a group G is a group of FINITE C-WIDTH if G has finite width with respect to all…

Let $G$ be a compact connected Lie group and let $P$ be a principal $G$-bundle over $K$. The gauge group of $P$ is the topological group of automorphisms of $P$. For fixed $G$ and $K$, consider all principal $G$-bundles $P$ over $K$. It is…

We prove that a finitely generated group contains a sequence of non-trivial elements which converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian.

We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan's property (T). Some of them are significantly shorter than the previously known shortest examples. Moreover, we show that some of those…

We characterize the group property of being with infinite conjugacy classes (or icc, in which all conjugacy classes beside 1 are infinite) for extensions of some specific groups ; namely extensions of abelian, centerless, icc, or word…

Part 1 : We remark that the conjugacy problem for pairs of hyperbolic au- tomorphisms of a finitely presented group (typically a free group) is decidable. The solution that we propose uses the isomorphism problem for the suspensions, and…

We classify the groups quasi-isometric to a group generated by finite-order elements within the class of one-ended hyperbolic groups which are not Fuchsian and whose JSJ decomposition over two-ended subgroups does not contain rigid vertex…

Tkachenko and Yaschenko [34] characterized the abelian groups G such that all proper unconditionally closed subsets of G are finite, these are precisely the abelian groups G having cofinite Zariski topology (they proved that such a G is…

We show that finitely generated mapping tori of free groups have a canonical collection of maximal sub-mapping tori of finitely generated free groups with respect to which they are relatively hyperbolic and locally relatively quasi-convex.…

We construct the first examples of finitely presented groups with cubic Dehn function containing a finitely generated infinite torsion subgroup. Moreover, we show that any infinite free Burnside group with sufficiently large odd exponent…

We study model geometries of finitely generated groups. If a finitely generated group does not contain a non-trivial finite rank free abelian commensurated subgroup, we show any model geometry is dominated by either a symmetric space of…

It is proved that for any prime $p$ a finitely generated nilpotent group is conjugacy separable in the class of finite $p$-groups if and only if the torsion subgroup of it is a finite $p$-group and the quotient group by the torsion subgroup…