  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. In particular, we show that if a finitely generated group G
contains an infinite finitely generated commensurated subgroup Q of infinite
index in G, then G is semistable at infinity. If additionally G and Q are
finitely presented and either Q is 1-ended or the pair (G,Q) has one filtered
end, then G is simply connected at infinity. This result leads to a relatively
short proof of V. M. Lew's theorem that finitely presented groups with infinite
finitely generated subnormal subgroups of infinite index are semistable at
infinity.
