We show, in particular, that, if a finite group $H$ is retract of any containing as verbally closed subgroup, then the centre direct factor $H$.

We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by Bergman. Our main result is that G is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that ω1-existentia...

we study a new class of $h_v$-structures called fundamentally very thin. this is an extension of the well known class of the very thin hyperstructures. we present applications of these hyperstructures.

We study a new class of $H_v$-structures called Fundamentally Very Thin. This is an extension of the well known class of the Very Thin hyperstructures. We present applications of these hyperstructures.

Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space. Furthermore, we show that none the conditions can be weakened.

Mixing in a natural way the notions of fully inert (see [6]) and strongly invariant (see [4]) subgroups of Abelian groups, we introduce the strongly inert subgroups which we determine for several classes of Abelian groups. Mathematics Subject Classification (2010). 20K27, 20K30, 20K10.

In the present note, we discuss certain observations made by the author in February 2009 concerning strongly torsion-free profinite groups [cf. [Mzk2], Definition 1.1, (iii)]. These observations grew out of e-mail correspondences between the author, Akio Tamagawa, and Marco Boggi, as well as oral discussions between the author and Akio Tamagawa. Definition 1. Let G be a profinite group. (i) We ...

Beauville surfaces are a class of complex surfaces defined by letting a finite group G act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the group G. A particularly interesting subclass are the ‘strongly real’ Beauville surfaces that have an analogue of complex conjugation defined on them. In this sur...

In this paper we show that all Garside groups are strongly translation discrete, that is, the translation numbers of non-torsion elements are strictly positive and for any real number r there are only finitely many conjugacy classes of elements whose translation numbers are less than or equal to r. It is a consequence of the inequality “infs(g) 6 infs(g n) n < infs(g) + 1” for a positive intege...

Let T be an almost strongly minimal theory. Work inside a monster model M of T . Let M be a model (a small elementary substructure of M). If G is an M -definable group, and H is an M -definable subgroup, we can consider the homogeneous space G/H with the left-action by G. We will define “etale cohomology groups” H M(G/H,A) for all n ≥ 0 and all abelian groups A. We would like the following thin...