a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the center of such...

As a motivation, we first recall the possible connection of electric-magnetic duality to finiteness in N = 1 super-Yang-Mills theories (SYM). Then, we present the criterion for all-order finiteness (i.e., vanishing of the β-functions at all orders) in N = 1 SYM. Finally, we apply this finiteness criterion to an SU(5) SGUT. The latter turns out to be all-order finite if one imposes additional sy...

This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from Coh to Fin commuting with the additive and multiplicative structure of linear logic. What makes this correspondence possible and conceptually interesting is the use of the infinite Ramsey theorem. Along the way, the question of the cardinality of the collection of finiten...

we discuss whether finiteness properties of a profinite group $g$ can be deduced from the coefficients of the probabilisticzeta function $p_g(s)$. in particular we prove that if $p_g(s)$ is rational and all but finitely many non abelian composition factors of $g$ are isomorphic to $psl(2,p)$ for some prime $p$, then $g$ contains only finitely many maximal subgroups.

The joint spectral radius of a finite set of real d × d matrices is defined to be the maximum possible exponential rate of growth of long products of matrices drawn from that set. A set of matrices is said to have the finiteness property if there exists a periodic product which achieves this maximal rate of growth. J. C. Lagarias and Y. Wang conjectured in 1995 that every finite set of real d× ...

I will discuss some aspects of the treatment of finiteness in its various facets given in (1) in the nontransformational theories of Head-Driven Phrase Structure Grammar (HPSG) and Lexical-Functional Grammar (LFG).1 Due to the way that syntactic information is represented in these approaches, it can be stated at the outset that finiteness is considered to really be a property of a clause. From ...

This note investigate some finiteness properties of the category U of unstable modules. One shows finiteness properties for the injective resolution of finitely generated unstable modules. One also shows a stabilization result under Frobenius twist for Ext-groups.

The controlled finiteness obstruction and torsion are defined using controlled algebra, giving a more algebraic proof of the topological invariance of torsion and the homotopy finiteness of compact ANRs.

In this paper we use "ring changed'' Gorenstein homologicaldimensions to define Cohen-Macaulay injective, projective and flatdimensions. For doing this we use the amalgamated duplication of thebase ring with semi-dualizing ideals. Among other results, we prove that finiteness of these new dimensions characterizes Cohen-Macaulay rings with dualizing ideals.