Related papers: On Bounded Packing in Polycyclic Groups

A subset of a group is characteristic if it is invariant under every automorphism of the group. We study word length in fundamental groups of closed hyperbolic surfaces with respect to characteristic generating sets consisting of a finite…

Let R be a class of groups closed under taking semidirect products with finite kernel and fully residually R-groups. We prove that R contains all R-by-{finitely generated residually finite} groups. It follows that a semidirect product of a…

We prove that the minimal representation dimension of a direct product $G$ of non-abelian groups $G_1,\ldots,G_n$ is bounded below by $n+1$ and thereby answer a question of Ab\'ert. If each $G_i$ is moreover non-solvable, then this lower…

On the projective plane there is a unique cubic root of the canonical bundle and this root is acyclic. On fake projective planes such root exists and is unique if there are no 3-torsion divisors (and usually exists, but not unique,…

It is shown that the Cuntz semigroup of a space with dimension at most two, and with second cohomology of its compact subsets equal to zero, is isomorphic to the ordered semigroup of lower semicontinuous functions on the space with values…

We show that a central extension of locally quasiconvex subgroup separable hyperbolic group is product separable, so long as it is subgroup separable. We also establish that a central extension of a double coset separable group by a…

In this paper is proved that the group of automorphisms of semigroup End(P[X]), if P is algebraically closed field, is generated by semi-inner automorphisms.

The problem of finding upper bounds for minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic $2$-groups. We show that for any natural $n\ge 2$ there is an undirected graph…

We show that a free-by-cyclic group with a polynomially growing monodromy is subgroup separable exactly when it is virtually $F_n \times \mathbb{Z}$. We also prove that random deficiency 1 groups are not subgroup separable with positive…

A sphere packing bound (SPB) with a prefactor that is polynomial in the block length $n$ is established for codes on a length $n$ product channel $W_{[1,n]}$ assuming that the maximum order $1/2$ Renyi capacity among the component channels,…

A scale-multiplicative semigroup in a totally disconnected, locally compact group $G$ is one for which the restriction of the scale function on $G$ is multiplicative. The maximal scale-multiplicative semigroups in groups acting…

We extend a recent result that for the (additive) semigroup of positive integers $\mathbb{N}$, there are continuum many subdirect products of $\mathbb{N} \times \mathbb{N}$ up to isomorphism. We prove that for $U,V$ each one of $\mathbb{Z}$…

We investigate the local dynamics of a proper superattracting holomorphic germ $f$ in $(\mathbb{C}^2,0)$ possessing a totally invariant line $L$ such that $f^*L = d L$ with $d\ge 2$, and such that $f|_L$ has a superattracting fixed point at…

The main result of this paper is that the outer automorphism group of a free product of finite groups and cyclic groups is semistable at infinity (provided it is one ended) or semistable at each end. In a previous paper, we showed that the…

We prove that if F is a finitely generated free group and f:F -> F is an automorphism with polynomial growth of degree d, then there exists a characteristic subgroup S < F of finite index such that the induced automorphism of the…

We study some fundamental properties of semicocycles over semigroups of self-mappings of a domain in a Banach space. We prove that any semicocycle over a jointly continuous semigroup is itself jointly continuous. For semicocycles over…

The main goal of this paper is a detailed study of asymptotic cones of the mapping class groups. In particular, we prove that every asymptotic cone of a mapping class group has a bi-Lipschitz equivariant embedding into a product of real…

We prove that any ascending chain of bounded rank subgroups in the fundamental group of a compact $3$-manifold stabilizes. We use geometrization to reduce the proof to fundamental groups of complete, finite-volume hyperbolic $3$-manifolds.…

Let $G$ be a torsion-free hyperbolic group and $\alpha$ an automorphism of $G$. We show that there exists a canonical collection of subgroups that are polynomially growing under $\alpha$, and that the mapping torus of $G$ by $\alpha$ is…

We explain some interesting relations in the degree three bounded cohomology of surface groups. Specifically, we show that if two faithful Kleinian surface group representations are quasi-isometric, then their bounded fundamental classes…