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The query [[Proves property satisfaction of::Abelian group]] was answered by the SMWSQLStore3 in 0.0076 seconds.


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 UsesFact about
Automorphism sends more than three-fourths of elements to inverses implies abelianSubgroup of size more than half is whole group
Abelian implies universal power map is endomorphism
Commuting fraction more than five-eighths implies abelianCyclic over central implies abelian
Lagrange's theorem
Subgroup of size more than half is whole group
Commuting fraction (2)
Finite abelian group (?)
Number of conjugacy classes (2)
FZ-group (2)
Abelian group (3)
Cube map is endomorphism iff abelian (if order is not a multiple of 3)Abelian implies universal power map is endomorphism
Cube map is surjective endomorphism implies abelian
Kth power map is bijective iff k is relatively prime to the order
Cube map (?)
Abelian group (?)
Cube map is surjective endomorphism implies abelianGroup acts as automorphisms by conjugation
Nth power map is surjective endomorphism implies (n-1)th power map is endomorphism taking values in the center
Square map is endomorphism iff abelian
Cube map (?)
Cyclic implies abelianCyclic group (2)
Abelian group (2)
Endomorphism sends more than three-fourths of elements to squares implies abelianSubgroup of size more than half is whole group
Abelian implies universal power map is endomorphism