Related papers: Deep pockets in lattices and other groups

Since a black hole does not emit light from its interior, nor does it have a surface on which light from nearby sources can be reflected, observational study of black hole physics requires observing the gravitational impact of the black…

The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of…

We show that for many classical knots one can find generalized torsion in the fundamental group of its complement, commonly called the knot group. It follows that such a group is not bi-orderable. Examples include all torus knots, the…

We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called {\em weakly maximal} representations. We prove that weakly maximal representations are discrete and injective and we describe…

(Abridged) Fossil systems are group- or cluster-sized objects whose luminosity is dominated by a very massive central galaxy. In the current cold dark matter scenario, these objects formed hierarchically at an early epoch of the Universe…

A subgroup of a finite group is wide if each prime divisor of the group order divides the subgroup order. We obtain the description of finite soluble groups with no wide subgroups. We also prove that a finite soluble group with nilpotent…

We prove several rigorous results about the asymptotic behaviour of the numbers of tadpoles (or lassos) embedded in a lattice, including cases where the head is subject to a constraint like being unknotted, or where the tail pierces the…

We introduce the class of \textit{Generalized Poincar\'{e}-Duality groups}: i.e, pro-$p$ groups of infinite rank which satisfy a Poincar\'{e}-duality. We prove some basic properties of Generalized Poincar\'{e}-Duality groups, and show that…

We give a solution stated in the title to problem 3 of part 1 of the problems listed in the book of Eklof and Mekler [EM],(p.453). There, in pp. 241-242, this is discussed and proved in some cases. The existence of strongly lambda-free ones…

We consider the logic space of countable (enumerated) groups and show that closed subspaces corresponding to some standard classes of groups have (do not have) generic groups. We also discuss the cases of semigroups and associative rings.

We develop the theory of distributive inverse semigroups as the analogue of distributive lattices without top element and prove that they are in a duality with those etale groupoids having a spectral space of identities, where our spectral…

This paper proves that the category of vacant n-tuple groupoids is equivalent to the category of factorizations of groupoids by n subgroupoids. Moreover it extends this equivalence to the category of maximally exclusive n-tuple groupoids,…

We prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk groups, where the problem is most difficult.

For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct non-large vector subspaces in the rational homology of finitely generated groups. The functorial properties of this…

In this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups. Using similar techniques, we show that every nontrivial normal subgroup of a…

Strongly real groups and totally orthogonal groups form two important subclasses of real groups. In this article we give a characterization of strongly real special 2-groups. This characterization is in terms of quadratic maps over fields…

We show that any group $G$ is contained in some sharply 2-transitive group $\mathcal{G}$ without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups $\mathcal{G}$ that we…

We classify what we call ``typically almost symmetric'' depth zero supercuspidal representations of classical groups into L-packets. Our main results resolve an ambiguity in the paper of Lust-Stevens \cite{Lust-Stevens} in this case, where…

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.

G.F. Voronoi (1868-1908) wrote two memoirs in which he describes two reduction theories for lattices, well-suited for sphere packing and covering problems. In his first memoir a characterization of locally most economic packings is given,…