If G is a word hyperbolic group of cohomological dimension 2, then every subgroup of G of type FP2 is also word hyperbolic. Isoperimetric inequalities are denned for groups of type FP2 and it is shown that the linear isoperimetric inequality in this generalized context is equivalent to word hyperbolicity. A sufficient condition for hyperbolicity of a general graph is given along with an applica...

We give a general framework connecing a branching time relation on nodes of a transition system to a final coalgebra for a suitable endofunctor. Examples of relations treated by our theory include bisimilarity, similarity, upper and lower similarity for transition systems with divergence, similarity for discrete probabilistic systems, and nested similarity. Our results describe firstly how to c...

This paper presents an experiment analyzing the behavior of modelers in interpreting conceptual model fragments developed using an OntologyDriven Conceptual Modeling Language (OntoUML). Our goal is to evaluate the effect of two ontological constructs (relator and role) in modeling relationships. Our hypotheses are: (i) the use of these constructs for modeling relations increases the clarity of ...

The tunnel number of a PL knot K is the minimum number of PL one-cells which must be attached in order that the regular neighborhood of the resulting complex has complement a handlebody [2]. It is easy to see that n-bridge knots have tunnel numbers (n 1) and torus knots have tunnel number one. More difficult is finding knots which have higher tunnel number. If a knot has tunnel number one, it w...

We study the asymptotic behaviour of a finitely presented Rees quotient S = Inv〈A | ci = 0 (i = 1, . . . , k) 〉 of a free inverse semigroup over a finite alphabet A. It is shown that if the semigroup S has polynomial growth then S is monogenic (with zero) or k ≥ 3. The three relator case is fully characterised, yielding a sequence of two-generated three-relator semigroups whose Gelfand-Kirillov...

We prove that the free Burnside Group B(3; 2) has order 27 and is isomorphic to ha; b j a3; b3(ab)3; (b 1a)3i. The technique of our proof is also used to show that ha; bja3; b3; a2(ba)nb2i is the semidirect product Cn2+n+1o C3.

By estimating the subgroup numbers associated with various classes of large groups, we exhibit a number of new phenomena in the theory of subgroup growth. Key-words: subgroup growth, large groups, one-relator groups, HNN-extensions MSC-Index: 20E07