= Compactly generated group
{wiki}
A topological group is compactly generated in the algebraic sense when a compact subset generates its underlying group. Adjoining its inverse and the identity gives a compact symmetric generating set $K$, and $G=\bigcup_{n\geq1}K^n$ is a <sigma-compact space>. Some conventions restrict the term to locally compact groups or require a compact generating neighbourhood; those stronger conventions supply local compactness. Compact generation by an arbitrary compact subset alone does not.
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