Representation Theory
Normal subgroups are special types of subgroups within a group where the subgroup is invariant under conjugation by any element of the group. This means that for any element in the group and any element in the normal subgroup, the result of conjugating the subgroup element by the group element will still be in the subgroup. This property is crucial for defining quotient groups and has deep implications in both representation theory and the study of character tables.
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