Some algebraic structure of the Riordan group

In this paper we highlight some of the algebraic properties of the Riordan group. We present some new properties and provide proofs for some known properties. For instance, proofs of properties of the power-Bell and derivative subgroups are presented. We also give a new property for generating stochastic Riordan matrices which are elements of the stochastic Riordan subgroup. Centralizers, stabilizers and certain Riordan group isomorphisms are also given and proved. We conclude by proving some properties connecting similar Riordan matrices and pseudo-involutions in the Riordan group.