]> 2026-07-15T15:12:13+00:00 Results with direct proofs 14 en Results with direct proofs Dedekind implies ACIC 0 en Dedekind implies ACIC Characteristic implies normal 0 en Characteristic implies normal Left cosets partition a group 0 en Left cosets partition a group Characteristicity is transitive 0 en Characteristicity is transitive Amalgam-characteristic implies potentially characteristic 0 en Amalgam-characteristic implies potentially characteristic Normal implies permutable 0 en Normal implies permutable Nilpotent implies solvable 0 en Nilpotent implies solvable Abelian implies ACIC 0 en Abelian implies ACIC NE implies weakly normal 0 en NE implies weakly normal Potentially characteristic implies normal 0 en Potentially characteristic implies normal Conjugacy-closed implies focal subgroup equals derived subgroup 0 en Conjugacy-closed implies focal subgroup equals derived subgroup Abelian implies nilpotent 0 en Abelian implies nilpotent Characteristic implies automorph-conjugate 0 en Characteristic implies automorph-conjugate Inner implies class-preserving 0 en Inner implies class-preserving Dedekind implies ACIC 0 en Dedekind implies ACIC Characteristic implies normal 0 en Characteristic implies normal Left cosets partition a group 0 en Left cosets partition a group Characteristicity is transitive 0 en Characteristicity is transitive Amalgam-characteristic implies potentially characteristic 0 en Amalgam-characteristic implies potentially characteristic Normal implies permutable 0 en Normal implies permutable Nilpotent implies solvable 0 en Nilpotent implies solvable Abelian implies ACIC 0 en Abelian implies ACIC NE implies weakly normal 0 en NE implies weakly normal Potentially characteristic implies normal 0 en Potentially characteristic implies normal Conjugacy-closed implies focal subgroup equals derived subgroup 0 en Conjugacy-closed implies focal subgroup equals derived subgroup Abelian implies nilpotent 0 en Abelian implies nilpotent Characteristic implies automorph-conjugate 0 en Characteristic implies automorph-conjugate Inner implies class-preserving 0 en Inner implies class-preserving INST 132 en INST