Marginality does not satisfy intermediate subgroup condition
This article gives the statement, and possibly proof, of a subgroup property (i.e., marginal subgroup) not satisfying a subgroup metaproperty (i.e., intermediate subgroup condition).
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It is possible to have a group and subgroups of such that and:
- is a marginal subgroup of .
- is not a marginal subgroup of .
Consider the following:
- is dihedral group:D8.
- is the center of dihedral group:D8.
- is one of the Klein four-subgroups of dihedral group:D8.
Then, we have:
- is marginal in , because center is marginal (it is marginal with respect to the variety of abelian groups).
- is not marginal in , because it is not characteristic in .