no small subgroup

{{Short description|Restriction on topological groups in mathematics}}

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.)