Related papers: Neretin groups admit no non-trivial invariant rand…

Let $G/\Gamma$ be the quotient of a semisimple Lie group by an arithmetic lattice. We show that for reductive subgroups $H$ of $G$ that is large enough, the orbits of $H$ on $G/\Gamma$ intersect nontrivially with a fixed compact set. As a…

We characterize when (and how) a Right-Angled Artin group splits nontrivially over an abelian subgroup.

We study finite groups $G$ having a normal subgroup $H$ and $D \subset G \setminus H, D \cap D^{-1}=\emptyset,$ such that the multiset $\{ xy^{-1}:x,y \in D\}$ has every non-identity element occur the same number of times (such a $D$ is…

We prove that the irreducible affine Coxeter groups are first-order rigid and deduce from this that they are profinitely rigid in the absolute sense. We then show that the first-order theory of any irreducible affine Coxeter group does not…

We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces cannot contain non-trivial self-affine sets.

In this paper we show that spectral analysis implies spectral synthesis for arbitrary varieties on locally compact Abelian groups, which have no discrete subgroup of infinite torsion free rank..

In this note, we show that an uncountable locally free group, and therefore every locally free group, has a free subgroup whose cardinality is the same as that of $G$. This result directly improve the main result in [T. Nishinaka,"Group…

In this paper, we demonstrate the non-existence of a computational algorithm capable of determining whether the second homotopy group of any compact constructive topological space is trivial. This finding shows the inherent limitations of…

For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group. It is generated by Dehn twists about two-sided simple closed curves. In this paper, we study involution generators of the twist subgroup. We…

We show that an infinite group is definable in any non trivial geometric $C$-minimal structure which is definably maximal and does not have any definable bijection between a bounded interval and an unbounded one in its canonical tree. No…

We give sufficient conditions for a subgroup of a tree almost automorphism group to be isomorphic to the topological full groups of a one-sided shift in the sense of Matui. As an application, we show that almost automorphism groups of trees…

Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with…

We address the problem to characterise closed type I subgroups of the automorphism group of a tree. Even in the well-studied case of Burger-Mozes' universal groups, non-type I criteria were unknown. We prove that a huge class of groups…

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…

It is an important problem in differential geometry to find non-naturally reductive homogeneous Einstein metrics on homogeneous manifolds. In this paper, we consider this problem for some coset spaces of compact simple Lie groups. A new…

We exhibit an infinite family of snowflake groups all of whose asymptotic cones are simply connected. Our groups have neither polynomial growth nor quadratic Dehn function, the two usual sources of this phenomenon. We further show that each…

For some very wide classes $\mathfrak{D}$ and $\mathfrak{B}\subset\mathfrak{D}$ of groups, the author proves that an arbitrary (nonabelian) group $G\in \mathfrak{D}$ (respectively $G\in \mathfrak{B}$) satisfies the minimal condition for…

This paper deals with naturally reductive pseudo-Riemannian 2-step nilpotent Lie groups $(N, \la \,,\,\ra_N)$, such that $\la \,,\,\ra_N$ is invariant under a left action. The case of nondegenerate center is completely characterized. In…

In this article, we prove that if all non-trivial cyclic subgroups of a group $G$ are self normalizing and $G$ satisfies the implication $$ \ o(x)\neq o(y)\Rightarrow o(xy)\neq o(x), o(y), $$ for all non-trivial elements $x$ and $y$, then…

We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…