In mathematics, especially in topology, a topological group G {\displaystyle G} is said to have no small subgroup if there exists a neighborhood U {\displaystyle U} of the identity that contains no nontrivial subgroup of G . {\displaystyle 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.)
See also Hilbert's fifth problem § No small subgroups
References
M. Goto, H., Yamabe, On some properties of locally compact groups with no small group