A set L with a binary operation(x,y)(→) x ○ y is called a loop if for any given a,b ∈ L the equations x○a = b,a○y = b have precisely one solutions x = b/a,y = a\b,and there is an element e∈ L with e○x = x○e = x for all x ∈ L.If L is a differentiable manifold,respectively a topological space such that the operations ○ : L×L → L,/: L×L → L,\ : L×L → L of L are differentiable,respectively continuous mappings,then we call it differentiable,respectively topological loop.A differentiable loop is called a geodesic loop if there exists an affine connection ▽ on the manifold L such that for any x,y ∈ L there are unique geodesics expe tX,expe tY with x = expe X,y = expe Y with x ○ y = expx ○τe,x(Y),where τe,x : TeL → TxL is the parallel translation along the geodesic expe tX.Specially,differentiable Bruck loops,Bol loops,left A-loops are realized on symmetric spaces,on totally geodesic submanifolds,on reductive homogeneous spaces.The left translations λx : L → L,y (→) x ○ y as well as the right translations ρx : L → L,y (→) y ○ x,x ∈ L,of a differentiable,respectively topological loop are diffeomorphisms,respectively homeomorphisms of L.We wish to discuss the questions which Lie groups can be represented as the group topologically generated by all left translations as well as by all left and right translations of a low-dimensional loop L.