7 papers · 1 filter
Three-dimensional topological loops with solvable multiplication groups
Ágota Figula
We prove that each -dimensional connected topological loop having a solvable Lie group of dimension as the multiplication group of is centrally nilpotent of clas…
Loops on spheres having a compact-free inner mapping group
Ágota Figula, Karl Strambach
We prove that any topological loop homeomorphic to a sphere or to a real projective space and having a compact-free Lie group as the inner mapping group is homeomorphic to the circ…
Bol loops as sections in semi-simple Lie groups of small dimension
Ágota Figula
Using the relations between the theory of differentiable Bol loops and the theory of affine symmetric spaces we classify all connected differentiable Bol loops having an at most $9…
The multiplication groups of 2-dimensional topological loops
Ágota Figula
We prove that if the multiplication group of a connected -dimensional topological loop is a Lie group, then is an elementary filiform nilpotent Lie group of…
Loops which are semidirect products of groups
Ágota Figula, Karl Strambach
We construct loops which are semidirect products of groups of affinities. As their elements in many cases one may take transversal subspaces of an affine space. In particular we ob…
Extensions of groups by weighted Steiner loops
Ágota Figula, Karl Strambach
Solving functional equations given in \cite{nagy} for extensions of a group by a weighted Steiner loop we obtain concrete description for all loops with interesting weak as…