Let $G$ be a group, and $\{G_1, G_2, \dots, G_n\}$ be subgroups such that "$G$ is generated by the subgroups $\{G_1, G_2, \dots, G_n\}$".
What does it mean for a group to be generated by a set of its subgroups?
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3It means that $G$ is generated by the union of the elements of those subgroups. – MJD Feb 19 '20 at 13:30
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1See also this post. – Dietrich Burde Feb 19 '20 at 14:01
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The only subgroup of $G$ containing $G_1, \dots, G_n$ is $G$ itself. – anomaly Feb 19 '20 at 14:13