# Characteristicity satisfies partition difference condition

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., characteristic subgroup) satisfying a subgroup metaproperty (i.e., partition difference condition)

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## Statement

Suppose is a group and is a subgroup of such that has a partition into subgroups , with containing at least two elements. Then, if all except possibly one of the is a characteristic subgroup of , all the s are characteristic subgroups of .