Subgroup

Conjugate subgroup

Two subgroups are conjugate to each other iff there exists such that 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.


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