# Semantic search

Abelian and ambivalent iff elementary abelian 2-group, Abelianization of ambivalent group is elementary abelian 2-group, Ambivalence is direct product-closed, Ambivalence is quotient-closed, Ambivalent and nilpotent implies 2-group, Ambivalent not implies strongly ambivalent, Automorphism group of simple non-abelian group need not be ambivalent, Center of ambivalent group is elementary abelian 2-group, Classification of ambivalent alternating groups, Complete not implies ambivalent, Conjugacy-closed subgroup of ambivalent group is ambivalent, Dihedral groups are ambivalent, Generalized dihedral groups are ambivalent, Normal subgroup of ambivalent group implies every element is automorphic to its inverse, Odd-order and ambivalent implies trivial, Projective special linear group of degree two is ambivalent iff -1 is a square, Special linear group of degree three or higher is not ambivalent, Special linear group of degree two is ambivalent iff -1 is a square, Symmetric groups are ambivalent