In mathematics, especially intopology, atopological group${\displaystyle G}$ is said to haveno small subgroup if there exists aneighborhood${\displaystyle U}$ of the identity that contains nonontrivial subgroup of${\displaystyle G.}$ An abbreviation '"NSS"' is sometimes used. A basic example of a topological group with no small subgroup is thegeneral linear group over the complex numbers.

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

• Hilbert's fifth problem § No small subgroups

• M. Goto,H., Yamabe,On some properties of locally compact groups with no small group

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