No small subgroup
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
Categories:
- Topology stubs
- Group theory
- Hilbert's problems
- Lie groups
- Topological groups