No small subgroup
Restriction on topological groups in mathematics
In mathematics, especially in topology, a topological group is said to have no small subgroup if there exists a neighborhood of the identity that contains no nontrivial subgroup of 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
References
- M. Goto, H., Yamabe, On some properties of locally compact groups with no small group
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