Multiplicative Invariants and the Finite Co-Hopfian Property

A group is said to be, finitely co-Hopfian when it contains no proper subgroup of finite index isomorphic to itself. It is known that irreducible lattices in semisimple Lie groups are finitely co-Hopfian. However, it is not clear, and does not appear to be known, whether this property is preserved under direct product. We consider a strengthening of the finite co-Hopfian condition, namely the existence of a non-zero multiplicative invariant, and show that, under mild restrictions, this property is closed with respect to finite direct products. Since it is also closed with respect to commensurability, it follows that lattices in linear semisimple groups of general type are finitely co-Hopfian

Parallizable manifolds and the fundamental group

ntroduction. Low-dimensional topology is dominated by the fundamental group. However, since every finitely presented group is the fundamental group of some closed 4-manifold, it is often stated that the effective influence of π1 ends in dimension three. This is not quite true, however, and there are some interesting border disputes. In this paper, we show that, by imposing the extra condition of parallelizability on the tangent bundle, the dominion of π1 is extended by an extra dimension

Remote sensing and interdisciplinary approach for studying Dubai’s urban context and development

Outlining the different phases and features of the urban and socio-economic development of Dubai, this work is aimed at highlighting the potential of remote sensing and the interdisciplinary approach for the study of cities characterised by overwhelming growth processes. In this way Dubai represents an ideal laboratory since the processes that have been triggered in the last decades have radically modified the previous balances and layouts. Thus the image of a mirage city has been gradually diffused, a city where ambitious objectives can be achieved, targets reached that are difficult to pursue elsewhere, frenetic development processes realised, in a nevertheless increasingly delicate territorial-environmental fabric onto which such phenomena are grafted. The analysis of various remote sensed images, gathered over different periods of times, highlights a number of important aspects from the geological point of view, of the physical geography, the urban development and the direct growth in all directions, with a series of artificial islands and much publicised anthropic works

Cancellation and stability properties of generalized torsion modules

Given a module X over a ring Λ its stability class consists of all modules X ′ such that X ⊕ Λ a ≅ X ′ ⊕ Λ b for some positive integers a , b . If the ring Λ is weakly finite then the stability class of a finitely generated Λ -module has the structure of a tree. We show that if, in addition, X is a generalized torsion module its stability class has the same shape as that of the zero module. In consequence we construct examples of nonprojective modules whose stability classes have arbitrarily large amounts of branching

Syzygies and diagonal resolutions for dihedral groups

We describe the syzygies of dihedral groups of order 4n+

The Way of Improvement Leads Home: Philips Vickers Fithian’s Rural Enlightenment

Offers a look at the life of Philip Vickers Fithian, a diarist from southern New Jersey, in an effort to assess the influence of the Enlightenment in the British American colonies. Profile of Fithian; His perception on personal morality and behavior; Political and social issues tackled in his journal; Efforts to reconcile the pursuit of Enlightenment self-improvement with passion and love for home

Syzygies and Minimal Resolutions

The essence of linear algebra over a field resides in the fact that every vector space is free; that is, has a spanning set of linearly independent vectors. The study of linear algebra over more general rings attempts to approximate this situation by the method of free resolutions. When a module M is not free we make a first approximation to its being free by taking a surjective homomorphism ∊ : F0 → M where F0 is free to obtain an exact sequence