Abstract: 

For a compact group $G$ with two closed subgroups $P, Q$ such that $P$ lies inside $Q$, it is known that the natural projection between the quotients $G/P$ and $G/Q$ is a Serre fibration, i.e., it has the homotopy lifting property with respect to every CW-complex. In this talk I will explain the steps taken to try to generalize this theorem to locally compact groups, although we will need to put some further conditions on its subgroups. I will prove that for a group $G$ with a closed locally compact almost connected subgroup $A$, the projection of $G$ onto $G/A$ is a Serre fibration.