Search results for "Transformation group"
showing 3 items of 3 documents
Locally compact (2, 2)-transformation groups
2010
We determine all locally compact imprimitive transformation groups acting sharply 2-transitively on a non-totally disconnected quotient space of blocks inducing on any block a sharply 2-transitive group and satisfying the following condition: if Δ1, Δ2 are two distinct blocks and Pi, Qi ∈ Δi (i = 1, 2), then there is just one element in the inertia subgroup which maps Pi onto Qi. These groups are natural generalizations of the group of affine mappings of the line over the algebra of dual numbers over the field of real or complex numbers or over the skew-field of quaternions. For imprimitive locally compact groups, our results correspond to the classical results of Kalscheuer for primitive l…
Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems
2011
International audience; This paper describes new ways to tackle several important problems encountered in geometric constraint solving, in the context of CAD, and which are linked to the handling of under- and over-constrained systems. It presents a powerful decomposition algorithm of such systems. Our methods are based on the witness principle whose theoretical background is recalled in a first step. A method to generate a witness is then explained. We show that having a witness can be used to incrementally detect over-constrainedness and thus to compute a well-constrained boundary system. An algorithm is introduced to check if anchoring a given subset of the coordinates brings the number …
Three-dimensional topological loops with nilpotent multiplication groups
2015
In this paper we describe the structure of indecomposable nilpotent Lie groups which are multiplication groups of three-dimensional simply connected topological loops. In contrast to the 2-dimensional loops there is no connected topological loop of dimension ≥ 3 such that the Lie algebra of its multiplication group is an elementary filiform Lie algebra. We determine the indecomposable nilpotent Lie groups of dimension ≤ 6 and their subgroups which are the multiplication groups and the inner mapping groups of the investigated loops. We prove that all multiplication groups have 1-dimensional centre and the corresponding loops are centrally nilpotent of class 2.