Central factor is not finite-join-closed
This article gives the statement, and possibly proof, of a subgroup property (i.e., central factor) not satisfying a subgroup metaproperty (i.e., finite-join-closed subgroup property).This also implies that it does not satisfy the subgroup metaproperty/metaproperties: Join-closed subgroup property (?), .
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Statement with symbols
Further information: Central factor
Example of the extraspecial group
For any prime , either of the two isomorphism classes of extraspecial groups of order gives a counterexample.