Incoherence and fibering of many free-by-free groups

G.C.H. implies existence of many rigid almost free abelian groups

This result has been generalized in various directions, e.g. replacing the ground ring Z by a more general ring and dropping the cardinal restriction (in Corner’s result this is actually |A| < 20), see [2], [20], [8], [9], [4], [23]. Other extensions include abelian groups which are not necessarily torsionfree, see Corner, Göbel [4] for references. Here we are interested in a different strength...

Complexity of Unification in Free Groups and Free Semi-groups

The exponent of periodicity is an important factor in estimates of complexity of word-unification algorithms. We prove that the exponent of periodicity of a minimal solution of a word equation is at most 2, where n is the length of the equation. Since the best known lower bound is 2 our upper bound is almost optimal and exponentially better than the original bound (6n) 2n4 + 2. Thus our result ...

Complex hyperbolic free groups with many parabolic elements

We consider in this work representations of the of the fundamental group of the 3-punctured sphere in PU(2, 1) such that the boundary loops are mapped to PU(2, 1). We provide a system of coordinates on the corresponding representation variety, and analyse more specifically those representations corresponding to subgroups of (3, 3,∞)-groups. In particular we prove that it is possible to construc...

HILBERTIAN FIELDS AND FREE PROFINITE GROUPS* by

Free and Forced Vibration Analysis of Functionally Graded Material Cylinders by a Mesh-Free Method

In this paper, free and forced vibration analysis of functionally graded material cylinders was carried out by mesh-free and finite element method. In this analysis, MLS shape functions are used for approximation of displacement field in the weak form of motion equation and essential boundary conditions are imposed by transformation method. Resulted set of differential equations are solved usin...