An algorithm for the word problem in extensions and the dependence of its complexity on the group representation
The Generalized Elliptic Curves are pairs , where is a family of triples of “points” from the set characterized by equalities of the form , where the law makes into a totally symmetric quasigroup. Isotopic loops arise by setting . When , identically is an entropic and is an abelian group. Similarly, a terentropic may be characterized by and is then a Commutative Moufang Loop . If in addition , we have Hall and is an exponent
Let G be a group, R an integral domain, and V G the R-subspace of the group algebra R[G] consisting of all the elements of R[G] whose coefficient of the identity element 1G of G is equal to zero. Motivated by the Mathieu conjecture [Mathieu O., Some conjectures about invariant theory and their applications, In: Algèbre non Commutative, Groupes Quantiques et Invariants, Reims, June 26–30, 1995, Sémin. Congr., 2, Société Mathématique de France, Paris, 1997, 263–279], the Duistermaat-van der Kallen...
For any real τ, a lim sup set WG,y(τ) of τ-(well)-approximable points is defined for discrete groups G acting on the Poincaré model of hyperbolic space. Here y is a 'distinguished point' on the sphere at infinity whose orbit under G corresponds to the rationals (which can be regarded as the orbit of the point at infinity under the modular group) in the classical theory of diophantine approximation.In this paper the Hausdorff dimension of the set WG,y(τ) is determined for geometrically finite groups...
Term substitution induces an associative operation on the free objects of any equational variety. In the case of left distributivity, the construction can be extended to any monogenic structure.