"Abelian normal is not join-closed"
"Ambivalent not implies strongly ambivalent"
"Central factor is not quotient-transitive"
"Cyclic normal is not join-closed"
"Endomorphism kernel is not transitive"
"Maximal among abelian characteristic not implies abelian of maximum order"
"Maximal among abelian characteristic not implies self-centralizing in nilpotent"
"Nilpotent not implies abelian"
"Quotient group need not be isomorphic to any subgroup"
"Rational not implies rational-representation"