No small subgroup

In mathematics, especially in topology, a topological group $$G$$ is said to have no small subgroup if there exists a neighborhood $$U$$ of the identity that contains no nontrivial subgroup of $$G.$$ An abbreviation '"NSS"' is sometimes used. A basic example of a topological group with no small subgroup is the general linear group over the complex numbers.

A locally compact, separable metric, locally connected group with no small subgroup is a Lie group. (cf. Hilbert's fifth problem.)