Abstract Let $$\Gamma$$ Γ be an arithmetic subgroup of $${{\,\mathrm{SU}\,}}(d,1)$$ SU ( d , 1 ) with cusps, and let $$X_\Gamma$$ X </mml:msub...

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

If G is a semidirect product N oH with N finitely generated then G has the property that every finite group is a quotient of some finite index subgroup of G if and only if one of N and H has this property. This has applications to 3-manifolds; for instance for any fibred hyperbolic 3-manifold M and any finite simple group S, there is a finite cyclic cover of M whose fundamental group surjects t...

Abstract Taking residual finiteness as a starting point, we consider three related properties: weak subsemigroup separability, strong separability and complete separability. We investigate whether each of these properties is inherited by Schützenberger groups. The main result this paper states that for finitely generated commutative semigroup S , conditions coincide are equivalent to every $\ma...

Two groups have a common model geometry if they act properly and cocompactly by isometries on the same proper geodesic metric space. We consider free products of uniform lattices in isometry rank-1 symmetric spaces prove, within each quasi-isometry class, that residually finite are abstractly commensurable. Our result gives first examples hyperbolic quasi-isometric but do not virtually geometry...

Definitions of finiteness are set-theoretical properties P such that, if the axiom of choice (AC) is assumed, a set satisfies P if and only if it is finite. It is well known that the equivalence of many definitions of finiteness (to one another, and to “ordinary” finiteness, defined below) requires some (perhaps weaker) form of AC. Thus, it is of interest to study how various definitions of fin...

I present a criterion for all-order finiteness in N =1 SYM theories. Three applications are given; they yield all-order finite N=1 SYM models with global symmetries of the superpotential. 1. INTRODUCTION The aim of this paper is to present applications of the criterion for all-order finiteness in N = 1 SYM of [ 1]. All-order finiteness is here meant in the sense of exact vanishing of the pertur...