Strict characteristicity is quotient-transitive
This article gives the statement, and possibly proof, of a subgroup property (i.e., strictly characteristic subgroup) satisfying a subgroup metaproperty (i.e., quotient-transitive subgroup property)
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Quotient-balanced implies quotient-transitive. Other special cases of this are:
- Characteristicity is quotient-transitive
- Normality is quotient-transitive
- Full invariance is quotient-transitive
Given: Groups such that is strictly characteristic in and is strictly characteristic in .
To prove: is strictly characteristic in .