Superperfectness is finite direct product-closed
This article gives the statement, and possibly proof, of a group property (i.e., superperfect group) satisfying a group metaproperty (i.e., finite direct product-closed group property)
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Statement for two groups
Statement for finitely many groups
Since the smallest nontrivial superperfect group is SL(2,5) which has order 120, the smallest nontrivial example of a superperfect group obtained as a direct product of smaller superperfect groups is the direct product of SL(2,5) and SL(2,5), which is a group of order 14400.
Proof for two groups
The proof basically follows from Fact (1), which allows us to compute the homology groups of a direct product in terms of the homology groups of the direct factors.
Proof for finitely many groups
This follows from the proof for two groups and using mathematical induction.