No small subgroup

This article will explore the impact and relevance of No small subgroup in different areas of contemporary society. Since its emergence, No small subgroup has played a fundamental role in people's lives, influencing cultural, social, economic and political aspects. Throughout history, No small subgroup has been an object of study and interest, generating debates and reflections on its importance and meaning. Through a critical analysis, we will seek to better understand the influence of No small subgroup in various spheres, as well as its present and future in an increasingly interconnected and interdependent world.

Restriction on topological groups in mathematics

In mathematics, especially in topology, a topological group ${\displaystyle G}$ is said to have no small subgroup if there exists a neighborhood ${\displaystyle U}$ of the identity that contains no nontrivial subgroup of ${\displaystyle G.}$ 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

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