We examine the computational complexity of some problems from algebraic automata theory and from the field of communication complexity: testing Green’s relations (relations that are fundamental in monoid theory), checking the property of a finite monoid to have only Abelian subgroups, and determining the deterministic communication complexity of a regular language. By well-known algebraizations...

We exhibit an interesting Cayley graph X of the elementary abelian group Z6 2 with the property that Aut(X) contains two regular subgroups, exactly one of which is normal. This demonstrates the existence of two subsets of Z6 2 that yield isomorphic Cayley graphs, even though the two subsets are not equivalent under the automorphism group of Z6 2 . 2000 Mathematics subject classification: 05C25.

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability ...

Studies of the circadian rhythm in plasma 11-O.H.C.S. levels showed that a subgroup of affective psychotics had higher plasma 11-OHCS values as compared with schizophrenic and other psychotic subgroups, and a somewhat less regular rhythm. One patient with depression who was studied over 48-hour periods showed a reduction in plasma 11-OHCS levels with clinical recovery. An accentuated fall and r...

The decomposition of unitary representations of a discrete group obtained by induction from a subgroup involves commensurators. In particular Mackey has shown that quasi-regular representations are irreducible if and only if the corresponding subgroups are self-commensurizing. The purpose of this work is to describe general constructions of pairs of groups ? 0 < ? with ? 0 its own commensurator...

We describe under various conditions abelian subgroups of the automorphism group Aut(Tn) of the regular n-ary tree Tn, which are normalized by the n-ary adding machine τ = (e, . . . , e, τ)στ where στ is the n-cycle (0, 1, . . . , n− 1). As an application, for n = p a prime number, and for n = 4, we prove that every soluble subgroup of Aut(Tn), containing τ is an extension of a torsion-free met...

This is a survey and announcement of recent results on the structure of free profinite semigroups using techniques and results from symbolic dynamics. The intimate connection between uniformly recurrent infinite words and J -maximal regular J -classes is explored to compute the maximal subgroups of the J -classes associated with Arnoux-Rauzy infinite words, which turn out to be free profinite g...

The (.)reg construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)reg which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J-order structure). We show that (S)reg can be described by a rather simple complete string rewrite system, as a consequence of which we obtain a new proof of the normal form theorem for (S)...

Let be a finitely generated abelian-by-finite group and k a field of characteristic p 0. We show that the Euler class of over k has finite order if and only if every p-regular element of has infinite centralizer in . We also give a lower bound for the order of the Euler class in terms of suitable finite subgroups of . This lower bound is derived from a more general result on finite-dimensional ...

We study the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces with respect to morphisms of a particular kind. We obtain upper bounds for the arithmetic self-intersection number of the dualizing sheaf on minimal regular models of the modular curves associated with congruence subgroups Γ0(N) with square free level, as well as for the modular curves X(N) and the Fe...