1.6.67 Fields, Groups, Rings

\( \underline{\mathrm{y}_{\text {word: }}} \) Prove that the subgroup generated by some class of conjugate elements of the group \( G \) is a normal subgroup of \( G \). Note. The converse is also true: a normal subgroup, together with each of its elements, contains the entire class of elements conjugate to it.