Given that a connected Lie group $G$ with nilpotent radical acts transitively by isometries on a connected Riemannian manifold $M$, the structure of the full connected isometry group $A$ of $M$ and the imbedding of $G$ in $A$ are described. In particular, if $G$ equals its derived subgroup and its Levi factors are of noncompact type, then $G$ is normal in $A$. In the special case of a simply transitive action of $G$ on $M$, a transitive normal subgroup $G^{\text{'}}$ of $A$ is constructed with $dim{G}^{\text{'}}=dimG$ and a sufficient condition is given...

We show that each element in the semigroup $S_n$ of all $n\times n$ non-singular upper (or lower) triangular stochastic matrices is generated by the infinitesimal elements of $S_n$, which form a cone consisting of all $n\times n$ upper (or lower) triangular intensity matrices.

We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M G. Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup.