- Let $G$ be a locally compact group without small subgroups. Is $G$ a "finite" dimensional Lie group? (i.e, $G$ is not infinite dimensional Lie group.)
- Are Lie groups precisely the locally Euclidean topological groups?

I need exact answer and exact references for the above questions. Thanks a lot for your answers.

has no small subgroupsif there is a neighborhood $U$ of the identity such that no nontrivial subgroup of $G$ is contained in $U$. By Gleason-Yamabe-Montgomery-Zippin, a locally compact group with no small subgroups is isomorphic to a real analytic Lie group (of finite dimension, with an arbitrary number of components). – YCor Feb 11 '13 at 21:26