In mathematics, especially in topology

Topology

Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

, a topological group

Topological group

In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology. A topological group is a mathematical object with both an algebraic structure and a...

 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

General linear group

In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible...

 over the complex numbers.

A locally compact, separable metric, locally connected

Locally connected space

In topology and other branches of mathematics, a topological space X islocally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets.-Background:...

 group with no small subgroup is a Lie group. (cf. Hilbert's fifth problem

Hilbert's fifth problem

Hilbert's fifth problem, is the fifth mathematical problem from the problem-list publicized in 1900 by mathematician David Hilbert, and concerns the characterization of Lie groups. The theory of Lie groups describes continuous symmetry in mathematics; its importance there and in theoretical physics...

.)