A subgroup Q is commensurated in a group G if each G conjugate of Q
intersects Q in a group that has finite index in both Q and the conjugate. So
commensurated subgroups are similar to normal subgroups. Semistability and
simple connectivity at infinity are geometric asymptotic properties of finitely
presented groups. In this paper we generalize several of the classic
semistability and simple connectivity at infinity results for finitely
presented groups.