"Automorph-conjugacy is centralizer-closed"
"Automorph-conjugacy is normalizer-closed"
"Automorph-conjugacy is not finite-conjugate-intersection-closed"
"Automorph-conjugacy is not finite-intersection-closed"
"Automorph-conjugacy is not finite-join-closed"
"Automorph-conjugacy is transitive"
"Characteristic implies automorph-conjugate"
"Endomorph-dominating not implies automorph-conjugate"
"Frattini's argument"
"Hall not implies automorph-conjugate"
"Hall not implies procharacteristic"
"Nilpotent not implies ACIC"
"Subgroup generated by commutator of generators of free group on two generators is automorph-conjugate"