Strict characteristicity is strongly join-closed

This article gives the statement, and possibly proof, of a subgroup property (i.e., strictly characteristic subgroup) satisfying a subgroup metaproperty (i.e., strongly join-closed subgroup property)
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Statement

Suppose $G$ is a group and $H_{i},i\in I$, is a collection of strictly characteristic subgroups of $G$, the join of subgroups $\langle H_{i}\rangle$ is also a strictly characteristic subgroup of $G$.

Related facts

• Endo-invariance implies strongly join-closed

Proof

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