Subgroup

Conjugate subgroup

Two subgroups are conjugate to each other iff there exists such that #m/def/group

This is a natural application of the Conjugation by an element to entire subgroup. If a subgroup is only conjugate to itself, it is called a Normal subgroup.

Properties

• Conjugate subgroups are isomorphic to each other, since conjugation is itself an automorphism on the supergroup.

#state/tidy | #lang/en | #SemBr