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Pure definability is transitive
From Groupprops
This article gives the statement, and possibly proof, of a subgroup property (i.e., purely definable subgroup) satisfying a subgroup metaproperty (i.e., transitive subgroup property)
View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties
Get more facts about purely definable subgroup | Get facts that use property satisfaction of purely definable subgroup | Get facts that use property satisfaction of purely definable subgroup| Get more facts about transitive subgroup property
Contents |
Statement
Verbal statement
A purely definable subgroup of a purely definable subgroup is purely definable.
Statement with symbols
Suppose 
are groups such that K is a purely definable subgroup of G and H is a purely definable subgroup of K. Then, H is a purely definable subgroup of G.
