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If $G$ is a group and $S$ is a subset of $G$, then $S$ is a set of generators if the smallest subgroup of $G$ containing $S$ equals $G$.

Equivalently, $S$ generates $G$ if \[ G=\bigcap_{S\subseteq H\leq G} H \,.\]

Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-07-07 20:43:55
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