,"Quick phrase","Defining ingredient"
"Category of groups",,"Group,Homomorphism of groups"
"Homomorphism of algebraic groups",,"Homomorphism of groups"
"Injective homomorphism",,"Homomorphism of groups,Trivial group"
"Normal subgroup","invariant under inner automorphisms, self-conjugate subgroup,same left and right cosets,kernel of a homomorphism,subgroup that is a union of conjugacy classes","Homomorphism of groups,Inner automorphism,Conjugate subgroups,Left coset of a subgroup,Right coset of a subgroup,Conjugacy class,Commutator of two subgroups"
"Normal-homomorph-containing subgroup",,"Normal subgroup,Homomorphism of groups"
"Simple group",,"Normal subgroup,Surjective homomorphism of groups,Homomorphism of groups,Trivial homomorphism,Subnormal subgroup,Simple group operator"
"Surjective homomorphism of groups",,"Homomorphism of groups,Category of groups"